The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^41+796x^42+1520x^43+2184x^44+2430x^45+2506x^46+2530x^47+1843x^48+1180x^49+678x^50+280x^51+146x^52+58x^53+34x^54+6x^55+2x^58+2x^60

The gray image is a code over GF(2) with n=368, k=14 and d=164.
This code was found by Heurico 1.16 in 1.78 seconds.