The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+72x^41+274x^42+208x^43+611x^44+488x^45+812x^46+464x^47+597x^48+264x^49+246x^50+32x^51+4x^52+8x^53+10x^54+1x^60+2x^62+2x^64

The gray image is a code over GF(2) with n=368, k=12 and d=164.
This code was found by Heurico 1.16 in 3.73 seconds.