The generator matrix

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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+110x^81+168x^82+270x^83+1066x^84+540x^85+732x^86+2190x^87+1158x^88+1254x^89+3802x^90+1740x^91+1962x^92+5404x^93+2172x^94+2484x^95+6700x^96+2808x^97+2628x^98+6368x^99+2364x^100+2310x^101+4416x^102+1320x^103+1104x^104+2000x^105+678x^106+330x^107+610x^108+156x^109+48x^110+88x^111+18x^112+32x^114+6x^117+4x^120+4x^123+2x^126+2x^129

The gray image is a linear code over GF(3) with n=144, k=10 and d=81.
This code was found by Heurico 1.16 in 33.6 seconds.