The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+23x^40+26x^42+64x^43+284x^44+64x^45+28x^46+11x^48+10x^50+1x^72

The gray image is a code over GF(2) with n=352, k=9 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.