The generator matrix

 1  0  0  0  1  1  1 X^2 X^3 X^3+X^2  1  1  1  1 X^3+X X^3  1  1  1  1  1  1  1 X^2+X  0 X^3+X X^2+X  X X^3+X X^3+X^2+X  1
 0  1  0  0 X^3  1 X^3+1  1  1  1 X^2+X X^3+X  1 X^2+1 X^3+X^2  1 X^3+X^2+X+1 X^3+X+1 X^3+X^2+X X^2 X^3+X^2+1 X^3 X^2+X+1 X^2+X  X  1 X^3+X^2+X  1  1  0  0
 0  0  1  0 X^3+1  1 X^3 X^3+X^2+1 X^2 X^3+X+1  1 X^3  X X^3+X^2+X+1  1 X^3+X^2+1 X^3+X^2+X+1 X^2+X+1 X^3+1 X^2+1  X X^3+X  0  1  1 X^3+1  1 X^3+X+1 X^2+1 X^3+X^2 X^3+X^2+X
 0  0  0  1  1 X^3 X^3+X^2+1 X^3+1  1 X^3+X X^3+X X+1 X^2+X X^3+X+1 X^3+X^2+X+1 X^2+X+1 X^2+X+1 X^3 X^2 X^2+X+1  0 X^2  1 X^3+X^2+X+1  1  X X^3+1  X X^2+1  1  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+350x^26+2260x^27+4074x^28+8254x^29+10962x^30+13322x^31+11771x^32+8316x^33+3618x^34+2008x^35+436x^36+134x^37+14x^38+10x^39+4x^40+2x^44

The gray image is a linear code over GF(2) with n=248, k=16 and d=104.
This code was found by Heurico 1.16 in 14.3 seconds.