The generator matrix

 1  0  0  1  1  1  0  X  1 X^2  1  1  X  1 X^2+X  1  X  0  1  1  1  1 X^2+X  1  1  1  1  1  X X^2+X  X
 0  1  0  0  1  1  1 X^2 X^2+1  1 X^2 X+1  1  X  1  X  1  1 X^2+1  1 X^2+X X+1  1 X^2+1 X^2+X+1  0 X^2+X X+1  1  1  0
 0  0  1  1 X^2 X^2+1  1  1  X X^2+X X^2+X X^2+1 X^2+X+1  1 X^2+1 X^2+X+1 X^2 X+1  X X^2+X+1 X^2  0 X^2+X X^2+1 X^2+X X^2 X^2 X+1 X+1 X^2  1
 0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  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 28.

Homogenous weight enumerator: w(x)=1x^0+233x^28+364x^30+218x^32+128x^34+39x^36+36x^38+5x^40

The gray image is a linear code over GF(2) with n=124, k=10 and d=56.
This code was found by Heurico 1.11 in 0.032 seconds.