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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+48x^86+64x^87+39x^88+64x^89+24x^90+7x^92+4x^94+4x^102+1x^116

The gray image is a linear code over GF(2) with n=352, k=8 and d=172.
This code was found by Heurico 1.16 in 1.19 seconds.