The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+194x^39+1095x^40+3218x^41+5612x^42+10510x^43+14272x^44+19816x^45+20870x^46+20408x^47+15299x^48+10538x^49+4948x^50+2710x^51+952x^52+404x^53+166x^54+34x^55+13x^56+8x^57+4x^58

The gray image is a code over GF(2) with n=368, k=17 and d=156.
This code was found by Heurico 1.16 in 92.6 seconds.