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

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+28x^82+60x^83+52x^84+86x^85+122x^86+108x^87+152x^88+134x^89+82x^90+82x^91+35x^92+18x^93+13x^94+16x^95+13x^96+2x^97+8x^98+6x^99+2x^100+3x^102+1x^164

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 0.599 seconds.