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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+30x^35+129x^36+196x^37+119x^38+30x^39+6x^40+1x^66

The gray image is a linear code over GF(2) with n=296, k=9 and d=140.
This code was found by Heurico 1.16 in 0.031 seconds.