The generator matrix

 1  0  1  1  1 X^3 X^2+X  1  1  1 X^3+X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1 X^3 X^3+X^2+1 X^2+X  1 X^3+1 X^2+X+1 X+1 X^3+X^2+X+1  1 X^2 X^3+X X^3+X  0  0 X^2+X X^3+X^2  X X^3+X^2+1 X^3+X^2 X^3+X^2 X^3+X^2+1  1 X^3+X+1  0
 0  0 X^2 X^3+X^2 X^3 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2 X^2 X^3  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2  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+53x^28+164x^29+187x^30+218x^31+184x^32+160x^33+51x^34+2x^35+2x^36+1x^38+1x^54

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 0.234 seconds.