The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+133x^84+84x^85+232x^86+80x^87+200x^88+48x^89+72x^90+16x^91+53x^92+16x^93+28x^94+18x^96+24x^100+12x^101+4x^102+1x^108+1x^112+1x^116

The gray image is a linear code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.11 in 0.328 seconds.