The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+776x^25+2224x^26+6990x^27+15108x^28+31642x^29+45432x^30+56850x^31+46600x^32+31742x^33+14795x^34+6900x^35+2066x^36+718x^37+134x^38+58x^39+16x^40+2x^41+7x^42+2x^43

The gray image is a linear code over GF(2) with n=248, k=18 and d=96.
This code was found by Heurico 1.16 in 199 seconds.