The generator matrix
1 0 1 1 1 X^2 1 1 X 1 1 X^2+X 1 1 X^2 1 1 0 1 1 X 1 1 X^2+X 1 1 X^2+X 1 1 0 1 X^2 1 1 X 1 1 X^2 1 X 1 1 X^2 1 X 1 X 1 1 0 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X X X^2 X X 0 X X
0 1 1 0 X+1 1 X^2+X+1 0 1 0 X^2+1 1 0 X^2+X+1 1 0 X+1 1 0 X^2+1 1 0 1 1 X X^2+X+1 1 X X^2+1 1 X^2+X 1 X+1 X^2+X 1 X^2+1 X 1 X 1 X^2+X+1 X 1 X 1 1 0 X^2+X+1 1 X X+1 X^2+X+1 1 X+1 X+1 X+1 1 X+1 X^2+X+1 X+1 X X^2+1 X^2+1 X^2+1 X^2+1 1 X^2+1 X^2 X^2 X^2 X^2 X^2+X X^2 X X^2 X X^2 X X^2 X^2 X^2+X 0 0 X^2 X^2+X X^2+X X X^2+X X^2 X 0 X^2
0 0 X 0 0 0 0 X X X X X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X X 0 0 X^2 X^2+X X X X^2 0 X^2 X^2+X X^2+X X^2+X X^2 0 0 X^2+X X X^2 X^2 X X^2+X 0 X X X^2 X^2+X 0 X^2+X X X^2+X X^2 X X^2+X X X^2+X X^2+X 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2+X X 0 X^2+X X X^2 X^2+X X^2 X^2 X X X^2 X X 0 0 0
0 0 0 X X^2 X^2+X X^2+X X X^2 X^2 X^2+X X X^2 0 X^2 X^2+X X X X^2+X X^2 X^2+X 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X 0 0 0 X^2+X X X^2+X X^2 X^2 X X^2 X^2 X X X^2 X^2+X X X X^2 X^2+X X^2+X X^2 X 0 X X X X^2+X X^2+X 0 X 0 X^2 X^2+X 0 0 X^2 X X^2 X^2 X^2+X X 0 X 0 0 X 0 X^2 X^2 0 X X X^2+X X 0 X X^2+X X^2+X X 0 X^2
generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.
Homogenous weight enumerator: w(x)=1x^0+288x^88+144x^90+276x^92+96x^94+146x^96+16x^98+28x^100+24x^104+4x^120+1x^128
The gray image is a linear code over GF(2) with n=368, k=10 and d=176.
This code was found by Heurico 1.16 in 0.521 seconds.