The generator matrix

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

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+273x^28+728x^29+832x^30+768x^31+553x^32+512x^33+258x^34+96x^35+61x^36+8x^37+4x^38+2x^42

The gray image is a linear code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 0.266 seconds.