The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+366x^32+1142x^33+2697x^34+3840x^35+5503x^36+5916x^37+5486x^38+3726x^39+2509x^40+994x^41+405x^42+96x^43+45x^44+28x^45+12x^46+2x^47

The gray image is a linear code over GF(2) with n=296, k=15 and d=128.
This code was found by Heurico 1.16 in 6.72 seconds.