The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+46x^37+136x^38+166x^39+103x^40+42x^41+15x^42+2x^43+1x^66

The gray image is a linear code over GF(2) with n=312, k=9 and d=148.
This code was found by Heurico 1.16 in 0.032 seconds.