The generator matrix

 1  0  0  0  1  1  1 2X  1  1  1  1  1 2X  1  1  0  1  X  0  1  1  X  1  1  X  1  1  1  1  1  1  1  0  1  1  1 2X  1  X  1  1  1 2X  1  1  1  X  0 2X  1
 0  1  0  0  0  1 2X+1  1  0  X 2X+2 2X+2 X+2  X 2X+1  2  1  X  1  1  2 2X+1  1 X+2 2X+1  1  1 2X+2  0 X+1 2X 2X+1 X+2  1 2X+2 2X  X  X 2X  X X+2  X X+1  1  2 2X+1  1  1  1  1  0
 0  0  1  0  1  1 2X+2 2X+1 X+1 2X+2 2X X+1  0  1 X+1  1  0 2X 2X+2 X+1  2  2 2X X+2  0 X+1  2  1 2X X+1  1  X  X 2X+2  2 2X+1  0  1 X+1  X  1 2X+1 2X+2  0  0  X  1 X+2  1 2X+2  X
 0  0  0  1  2  0 2X+2 2X+2 2X+1 2X X+1 2X  2 X+1  1  2  1  1 2X+2 X+1 2X+1 2X  2 X+2 X+1 2X 2X+1 X+1 2X+2 2X+2  0 2X+2  2 2X+1  X 2X+2  1  2 2X+1  1  2 2X  2  2  X 2X+2  0 2X+1  1  2  0
 0  0  0  0 2X  0 2X 2X  X  0  X  0 2X  X  X 2X  X  X  X 2X 2X 2X  X  0 2X 2X  0  0  0  0 2X  0  X 2X  X  X 2X 2X 2X  0  X 2X  0  0  0  X  X  0  X 2X  0
 0  0  0  0  0  X  X  0 2X 2X 2X  0  X  X  X 2X  0  0  X  X  X  0 2X  0 2X  X 2X  X 2X 2X 2X  X  0  0  0  0 2X 2X  0 2X 2X  X 2X 2X  X 2X  X 2X 2X 2X  X

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+176x^87+210x^88+300x^89+854x^90+780x^91+1092x^92+1770x^93+1500x^94+1812x^95+2848x^96+2352x^97+2448x^98+3568x^99+2970x^100+3552x^101+4728x^102+3594x^103+3312x^104+4496x^105+2988x^106+2742x^107+3372x^108+2004x^109+1506x^110+1560x^111+900x^112+600x^113+544x^114+174x^115+126x^116+92x^117+24x^118+6x^119+18x^120+14x^123+6x^126+6x^129+4x^132

The gray image is a linear code over GF(3) with n=153, k=10 and d=87.
This code was found by Heurico 1.16 in 36.3 seconds.