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  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1 X^2  X
 0 X^3+X^2  0 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^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0  0 X^3 X^3 X^2 X^3 X^2 X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3  0  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3
 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 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  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+22x^37+44x^38+128x^39+46x^40+8x^41+4x^46+1x^48+2x^53

The gray image is a linear code over GF(2) with n=312, k=8 and d=148.
This code was found by Heurico 1.16 in 0.047 seconds.