The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+598x^26+1438x^28+2109x^30+2065x^32+1372x^34+522x^36+74x^38+6x^40+6x^42+1x^46

The gray image is a linear code over GF(2) with n=124, k=13 and d=52.
This code was found by Heurico 1.11 in 101 seconds.