The generator matrix

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

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+211x^26+930x^27+2351x^28+3630x^29+6009x^30+6422x^31+6190x^32+3870x^33+2045x^34+678x^35+311x^36+82x^37+23x^38+2x^39+9x^40+2x^41+2x^44

The gray image is a linear code over GF(2) with n=248, k=15 and d=104.
This code was found by Heurico 1.16 in 5.47 seconds.