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  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  2 3X 2X  X  2 X+2  X  0  2 3X+2 3X+2 2X 2X+2 3X 3X  0 3X+2 3X+2  0  2  2 3X 3X 2X 2X 2X 3X+2  2 X+2 X+2 2X+2  0 3X+2 2X 2X+2 X+2
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X 2X 2X+2  2 2X+2  2 2X+2  0  0  0 2X+2 2X+2  2  0  2 2X  2 2X  2 2X+2 2X 2X  2 2X  2  0 2X+2  2 2X  0 2X 2X+2  0  2 2X  2
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+78x^43+47x^44+184x^45+416x^46+172x^47+46x^48+72x^49+6x^51+1x^52+1x^88

The gray image is a code over GF(2) with n=368, k=10 and d=172.
This code was found by Heurico 1.16 in 0.11 seconds.