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 2X+2 2X+2
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2  2  2  0  2  0  2  0  2 2X 2X+2  0 2X  2  2
 0  0 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X
 0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0

generates a code of length 46 over Z4[X]/(X^2+2X+2) 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 8.61 seconds.