The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+386x^34+832x^35+548x^36+724x^37+634x^38+568x^39+187x^40+84x^41+81x^42+32x^43+16x^44+2x^46+1x^50

The gray image is a linear code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 0.36 seconds.