The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 2X 1 1 1 1 1 0 1 X 1 1 1 1 1 0 1 1 2X 1 1 2X 1 1 0 1 1 1 1 1 1 0 1 1 1 2X 1 1 1 1 1 1 1 2X 1 1 1 2X 1 1 X 1 1 0 0 1 1 2X 1 1 1 1 0 1 2X 1 2X 1 1 1 2X 1 0 0 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 X+1 0 2 1 X 1 2X+1 2 2 2X+1 0 1 0 1 2X+2 1 X 1 2 1 X 2X+1 1 2X+2 X+2 1 X 1 1 X+2 2X+1 X+2 2 X+1 0 1 X+1 X 1 1 2X X+2 X+2 X+2 2X+2 X+1 X+1 1 2X 2X X+1 1 2X X 1 X+2 2X+2 1 1 2 2 1 2X+1 X 2 0 1 0 1 1 1 2 0 2X+1 1 X+1 1 1 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X 0 X 2X 2X X 2X 2X 2X 2X 0 2X 2X 0 X X 2X 0 2X X 0 0 2X 2X X X 0 2X 0 X 2X X 2X 0 X 2X 0 2X X X 2X 0 2X 2X 0 X X 0 0 2X X 2X X X 2X X 2X X X X 2X 0 0 0 0 X X X 2X 0 0 2X X 0 0 0 X 0 2X 0 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X X 2X 0 2X 0 0 0 X 2X 2X 2X X X X 2X 0 X 2X X X 2X 0 0 X 2X X X X 0 0 X X 0 2X 2X X 0 2X 2X X 0 X 2X 0 X 0 X 0 2X 2X 0 0 X 2X 2X X X X 0 0 2X 2X 0 2X 0 0 X 0 0 2X X 0 X 2X 0 2X 2X X 2X 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 2X 2X X 2X X X 2X X 0 0 2X 2X 0 0 0 2X X X 0 0 2X 2X 2X X 0 0 2X X X 0 0 0 2X X 0 0 X 2X 2X X 2X X 0 2X 2X 0 0 2X X 2X 0 2X 0 X 2X 2X 0 X X X X 2X X X 0 2X X 0 2X 0 X 0 2X X X 0 0 2X 2X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 0 X X X X 2X 0 2X X 0 X 0 2X 2X X X 2X 0 0 0 X X 2X 0 X X 0 X 2X 2X 0 2X 0 X X X X 2X X 0 X X X 2X 0 0 0 X 0 2X 0 2X 0 X 0 2X 2X 0 X 2X 2X 2X 0 2X 2X X 2X X X 2X 0 2X X 2X X 2X 0 X 0 X 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X X 2X X 0 X X 2X X X X X 0 0 X X 0 2X X 0 X 0 2X 0 0 2X 0 X 0 X 2X X 2X 0 2X 2X 0 2X X 2X 2X 0 X 2X 0 0 2X 2X 0 X 0 0 0 0 2X X 0 0 0 X 2X 2X X 0 2X 2X 2X 2X 0 X X 2X 2X 0 X 0 2X 2X 2X 0 X 0
generates a code of length 99 over Z3[X]/(X^2) who´s minimum homogenous weight is 177.
Homogenous weight enumerator: w(x)=1x^0+30x^177+208x^180+30x^181+54x^182+396x^183+132x^184+156x^185+690x^186+306x^187+330x^188+970x^189+384x^190+432x^191+1070x^192+546x^193+570x^194+1386x^195+624x^196+690x^197+1504x^198+654x^199+720x^200+1414x^201+672x^202+678x^203+1218x^204+552x^205+402x^206+958x^207+264x^208+252x^209+472x^210+162x^211+54x^212+268x^213+30x^214+36x^215+112x^216+18x^217+70x^219+58x^222+40x^225+32x^228+22x^231+12x^234+2x^237+2x^243
The gray image is a linear code over GF(3) with n=297, k=9 and d=177.
This code was found by Heurico 1.16 in 11.8 seconds.