The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+56x^26+176x^27+347x^28+282x^29+908x^30+636x^31+867x^32+294x^33+288x^34+112x^35+72x^36+30x^37+12x^38+4x^39+8x^40+2x^41+1x^44

The gray image is a linear code over GF(2) with n=248, k=12 and d=104.
This code was found by Heurico 1.16 in 0.157 seconds.