The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+256x^83+116x^84+366x^85+134x^86+318x^87+81x^88+168x^89+87x^90+160x^91+34x^92+106x^93+25x^94+62x^95+15x^96+44x^97+9x^98+28x^99+4x^100+20x^101+1x^102+8x^103+3x^104+2x^108

The gray image is a linear code over GF(2) with n=352, k=11 and d=166.
This code was found by Heurico 1.11 in 1.33 seconds.