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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+67x^42+228x^43+152x^44+520x^45+204x^46+440x^47+153x^48+176x^49+48x^50+36x^51+12x^52+8x^53+1x^58+2x^64

The gray image is a code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.