The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0
 0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0
 0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0
 0  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0  0  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0
 0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+43x^32+84x^36+64x^38+1688x^40+64x^42+52x^44+34x^48+16x^52+1x^56+1x^72

The gray image is a linear code over GF(2) with n=320, k=11 and d=128.
This code was found by Heurico 1.16 in 0.109 seconds.