The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1 X^2  1 X^2 X^2  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2  0  0 X^3+X^2  0 X^3 X^2 X^3 X^2 X^2 X^3 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2 X^2 X^3  0  0 X^3 X^3+X^2 X^3 X^2 X^2  0 X^3  0 X^2  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2  0
 0  0  0 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 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+74x^26+222x^28+32x^29+354x^30+704x^31+355x^32+32x^33+190x^34+57x^36+22x^38+4x^40+1x^52

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 0.078 seconds.