The generator matrix

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

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+30x^82+20x^83+54x^84+62x^85+44x^86+332x^87+158x^88+46x^89+153x^90+12x^91+26x^92+10x^93+20x^94+20x^95+17x^96+10x^97+8x^98+1x^170

The gray image is a linear code over GF(2) with n=352, k=10 and d=164.
This code was found by Heurico 1.16 in 0.688 seconds.