The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+112x^83+176x^84+148x^85+136x^86+122x^87+78x^88+34x^89+53x^90+36x^91+30x^92+26x^93+10x^94+2x^95+18x^96+14x^97+8x^98+16x^99+2x^101+1x^104+1x^114

The gray image is a linear code over GF(2) with n=348, k=10 and d=166.
This code was found by Heurico 1.16 in 0.412 seconds.