The generator matrix

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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+186x^82+366x^83+498x^84+1122x^85+1260x^86+1068x^87+1878x^88+2304x^89+1858x^90+2742x^91+3126x^92+2586x^93+3684x^94+4224x^95+2952x^96+4620x^97+4344x^98+2968x^99+3846x^100+3780x^101+2032x^102+2520x^103+1638x^104+978x^105+1062x^106+696x^107+312x^108+192x^109+126x^110+42x^111+18x^112+6x^113+6x^114+6x^120+2x^129

The gray image is a linear code over GF(3) with n=144, k=10 and d=82.
This code was found by Heurico 1.16 in 41.6 seconds.