The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  1 X^2+X X^2+X  1  1  X  1 X^2+X  1 X^2+X  1 X^2  X  1  1  1  1  1  1  X X^2+X  1  0 X^2+X  1 X^2  0  1 X^2+X  1 X^2 X^2  1  1  1 X^2 X^2+X  1  1  1  1  1 X^2  1  1  X  0  0  X  0  1  X  0  1  1 X^2+X  1 X^2+X  1 X^2+X  1  1 X^2  1  X  0 X^2 X^2+X  1  1  1 X^2+X  1
 0  1  0  0  0  1  1  1 X^2  1  1  0  1  1  0  X  X  1 X^2+1 X^2+X  1  1  1 X^2 X^2  0  0  1 X^2+X+1 X+1 X+1  X X+1 X+1  1  1 X^2  X  1 X^2+X  1  1 X+1 X^2 X^2+X+1  X  1 X^2+1  0 X^2  1 X^2+X  X X^2+X+1 X^2+1 X+1  1  0 X^2 X^2+X+1  1  X  1  1 X^2 X^2+X  1  1 X+1  1  X  0  1  0 X^2 X^2+X  X X^2+X  0 X^2+X X^2+X  1  1  1 X+1 X^2+1  1 X^2+X
 0  0  1  0  1 X^2 X^2+1  1  1  0  1 X^2  1  0 X^2+1 X^2  1  X X^2+X X^2+1 X^2+1  X X^2+1 X^2+X X^2 X^2+X+1  1 X^2 X^2+1 X^2+X+1  X X+1  0  1  1 X+1 X^2  1 X^2+X X^2+X+1 X^2 X^2+1 X^2 X^2+X  X  1 X^2+X X^2+1 X+1  X  X  1 X^2 X+1 X^2+X+1 X^2+X X^2+X+1  1  1  0 X^2+X  1  0  0  X  1 X^2+X+1 X+1 X^2+X+1  0  0 X+1 X^2+X+1 X^2+1  1 X^2 X^2+1  1  1  X  1 X^2+X+1 X^2+1 X+1 X+1  X X^2 X^2+1
 0  0  0  1 X^2  0 X^2 X^2  1  1 X^2+1  1  1 X^2+1 X^2+1 X^2+X X+1 X^2  0  0 X^2+X+1 X+1  0 X^2+X+1  1 X+1 X^2+X X^2+1 X^2+X X^2+X+1 X^2+1 X^2+1 X^2+X X^2+X+1  X X+1  X X^2+1  X  0 X^2+X+1  X X+1  1 X+1 X^2+X X^2  X X^2+X X^2+1 X^2+1  1  0  0  1  0 X^2+X X+1 X^2+X  1  1 X+1 X^2  0  1 X^2+X X^2+X X^2 X^2+1 X^2+X  1  0 X^2+1 X+1 X^2+X+1 X+1  1 X^2  X  1 X^2+X+1 X+1  1  0 X^2+X+1  X X^2+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+380x^82+818x^84+822x^86+686x^88+430x^90+330x^92+274x^94+165x^96+118x^98+44x^100+16x^102+4x^104+8x^106

The gray image is a linear code over GF(2) with n=352, k=12 and d=164.
This code was found by Heurico 1.11 in 1.55 seconds.