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.