The generator matrix

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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+114x^88+168x^89+30x^90+96x^91+90x^92+24x^93+66x^94+18x^95+22x^96+18x^97+18x^98+2x^99+12x^100+18x^101+6x^103+2x^105+12x^106+12x^107

The gray image is a linear code over GF(3) with n=138, k=6 and d=88.
This code was found by Heurico 1.13 in 0.0688 seconds.