The generator matrix

 1  0  1  1  1 X^2  X  1  1  1 X^2+X  1  1  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1 X^2  1  1 X^2  1  1 X^2  0  1  1  1 X^2+X  1  X  1 X^2  1  1 X^2+X  1 X^2+X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1 X^2  X  X X^2  1  1 X^2 X^2  1  1 X^2+X X^2  X
 0  1  1 X^2+X X^2+X+1  1  1 X+1  X X^2+1  1 X^2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X^2+X+1  1 X^2+X  1  1  1 X^2 X^2+X+1  X  1  1  1  0  1  0  X  1  X  1 X^2+X+1 X^2+1 X^2+X+1  1 X^2+X X+1 X^2+1 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X+1 X+1  1 X^2+1 X^2+X+1 X^2+1 X^2+X+1 X^2+1  0 X^2 X^2  0 X^2+X  X X^2 X^2  0 X^2+X X^2 X^2  X  X  X X^2+X  1  X  X  0  1  1  1
 0  0  X  0 X^2+X  X  X X^2  X X^2  0  X X^2+X X^2  0  0  X X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0  X  X  0  X X^2+X  0 X^2+X X^2 X^2+X  0 X^2  X  0  0  X  0 X^2+X  X  0 X^2 X^2  X  X X^2 X^2+X X^2+X X^2+X  X  0 X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2  0 X^2  0 X^2 X^2  X X^2+X  0 X^2  0 X^2  X X^2+X  X X^2+X X^2+X  X  0 X^2 X^2 X^2  X X^2  X  X X^2
 0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0
 0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  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+76x^83+63x^84+180x^85+55x^86+212x^87+37x^88+128x^89+35x^90+60x^91+33x^92+60x^93+21x^94+20x^95+8x^96+12x^97+1x^98+16x^99+1x^104+4x^113+1x^120

The gray image is a linear code over GF(2) with n=352, k=10 and d=166.
This code was found by Heurico 1.16 in 0.566 seconds.