The generator matrix

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

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+357x^42+778x^43+1164x^44+1496x^45+1269x^46+1096x^47+849x^48+488x^49+339x^50+202x^51+96x^52+32x^53+19x^54+4x^55+2x^56

The gray image is a code over GF(2) with n=368, k=13 and d=168.
This code was found by Heurico 1.16 in 0.484 seconds.