The generator matrix

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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+25x^44+6x^46

The gray image is a linear code over GF(2) with n=344, k=5 and d=176.
This code was found by Heurico 1.16 in 0.031 seconds.