The generator matrix

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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+22x^38+28x^40+32x^41+22x^42+832x^43+18x^44+32x^45+10x^46+11x^48+9x^50+6x^52+1x^82

The gray image is a linear code over GF(2) with n=344, k=10 and d=152.
This code was found by Heurico 1.16 in 0.563 seconds.