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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+45x^44+192x^45+15x^48+3x^60

The gray image is a linear code over GF(2) with n=360, k=8 and d=176.
This code was found by Heurico 1.16 in 0.032 seconds.