The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3 X^3 X^2 X^2 X^3  0 X^3+X^2 X^2  0 X^3 X^3 X^2 X^3
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3  0 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2  0  0 X^2 X^2 X^2 X^3
 0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0 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 34.

Homogenous weight enumerator: w(x)=1x^0+7x^34+12x^35+56x^36+360x^37+56x^38+12x^39+6x^40+1x^42+1x^72

The gray image is a linear code over GF(2) with n=296, k=9 and d=136.
This code was found by Heurico 1.16 in 0.032 seconds.