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.