The generator matrix

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

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+307x^28+200x^30+298x^32+152x^34+49x^36+17x^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 4.38 seconds.