The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+12x^38+96x^39+13x^40+2x^42+2x^44+1x^46+1x^54

The gray image is a linear code over GF(2) with n=312, k=7 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.