The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+134x^44+256x^46+110x^48+10x^52+1x^80

The gray image is a code over GF(2) with n=368, k=9 and d=176.
This code was found by Heurico 1.16 in 8.47 seconds.