The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  1 X^2  1  1 X^2  X  X  1  1 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^3 X^2  0  0 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3  0  0  0 X^3+X^2 X^2 X^3+X^2 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  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+57x^26+32x^27+207x^28+128x^29+403x^30+448x^31+401x^32+128x^33+125x^34+32x^35+48x^36+17x^38+14x^40+6x^42+1x^44

The gray image is a linear code over GF(2) with n=248, k=11 and d=104.
This code was found by Heurico 1.16 in 0.062 seconds.