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

generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+138x^89+288x^90+330x^91+702x^92+1200x^93+1152x^94+1356x^95+1992x^96+1716x^97+1896x^98+3116x^99+2436x^100+2724x^101+4456x^102+3366x^103+3288x^104+4418x^105+3498x^106+3138x^107+4274x^108+2760x^109+2436x^110+2864x^111+1638x^112+1290x^113+1072x^114+456x^115+444x^116+270x^117+144x^118+78x^119+62x^120+6x^122+16x^123+16x^126+4x^129+8x^132

The gray image is a linear code over GF(3) with n=156, k=10 and d=89.
This code was found by Heurico 1.16 in 37.4 seconds.