The generator matrix

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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+76x^87+42x^88+48x^89+236x^90+96x^91+96x^92+262x^93+96x^94+108x^95+212x^96+66x^97+132x^98+112x^99+120x^100+84x^101+174x^102+66x^103+18x^104+100x^105+18x^108+6x^111+6x^114+2x^117+8x^120+2x^123

The gray image is a linear code over GF(3) with n=144, k=7 and d=87.
This code was found by Heurico 1.16 in 0.0669 seconds.