The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 0 X^2+X 1 1 1 1 X^2 X 1 1 1 1 1 1 1
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 0 X^2+X X+1 X^2+1 1 1 X^2 X X^2+X+1 1 1 1 0 X^2 X^2 X X^2+X X 0
0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0
0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0
generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+80x^29+30x^30+32x^31+31x^32+80x^33+2x^46
The gray image is a linear code over GF(2) with n=124, k=8 and d=58.
This code was found by Heurico 1.16 in 0.0089 seconds.