The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+398x^31+1919x^32+4570x^33+9032x^34+15862x^35+21207x^36+24622x^37+21787x^38+16100x^39+9184x^40+4228x^41+1456x^42+470x^43+167x^44+46x^45+11x^46+2x^47+2x^48+6x^49+2x^50

The gray image is a linear code over GF(2) with n=296, k=17 and d=124.
This code was found by Heurico 1.16 in 66.5 seconds.