The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1 X^2 X^2  X X^2  X  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2  0 X^2 X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2
 0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+145x^28+96x^29+104x^30+320x^31+185x^32+96x^33+24x^34+43x^36+9x^40+1x^48

The gray image is a linear code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.719 seconds.