The generator matrix

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

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+242x^28+368x^30+185x^32+144x^34+46x^36+32x^38+6x^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 1.16 in 0.0386 seconds.