The generator matrix

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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+12x^88+6x^89+236x^90+120x^91+210x^92+888x^93+384x^94+480x^95+1710x^96+888x^97+1116x^98+3130x^99+1494x^100+1602x^101+4810x^102+2280x^103+2478x^104+6204x^105+2490x^106+2610x^107+6480x^108+2412x^109+2520x^110+5114x^111+1830x^112+1344x^113+2568x^114+822x^115+588x^116+1136x^117+348x^118+150x^119+350x^120+42x^121+18x^122+96x^123+54x^126+16x^129+6x^132+6x^135

The gray image is a linear code over GF(3) with n=159, k=10 and d=88.
This code was found by Heurico 1.16 in 37 seconds.