The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1 X^2  1  X  X  0  X X^2
 0  X  0  X  0  0 X^2+X X^2+X X^2+X  0 X^2 X^2+X  0 X^2  X  X X^2+X X^2 X^2  X  X X^2  0  0  X X^2 X^2+X  X  0  X  X
 0  0  X  X  0 X^2+X X^2+X  0  0 X^2  X X^2+X  0  X X^2+X X^2 X^2 X^2  X X^2+X  0  0  X  0 X^2+X X^2+X X^2 X^2  X  X X^2+X
 0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2  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+145x^28+104x^30+185x^32+24x^34+43x^36+9x^40+1x^48

The gray image is a linear code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.16 in 0.528 seconds.