The generator matrix

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

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+264x^88+600x^89+478x^90+1014x^91+1218x^92+1214x^93+1986x^94+2190x^95+1818x^96+3054x^97+3300x^98+2558x^99+3546x^100+3798x^101+2828x^102+4074x^103+4470x^104+2850x^105+3942x^106+3504x^107+2184x^108+2556x^109+1890x^110+1060x^111+1134x^112+648x^113+228x^114+264x^115+228x^116+78x^117+30x^118+24x^119+8x^120+6x^121+2x^126+2x^129

The gray image is a linear code over GF(3) with n=153, k=10 and d=88.
This code was found by Heurico 1.16 in 263 seconds.