The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1 X^2 X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X^2 X^2+X X^3+X X^3 X^3+X^2+X  0 X^3 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0  0  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  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+149x^28+386x^30+362x^32+76x^34+47x^36+2x^38+1x^56

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 0.031 seconds.