The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+388x^82+767x^84+886x^86+620x^88+512x^90+340x^92+244x^94+161x^96+60x^98+77x^100+22x^102+18x^104

The gray image is a linear code over GF(2) with n=352, k=12 and d=164.
This code was found by Heurico 1.16 in 5.18 seconds.