The generator matrix

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

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+94x^41+234x^42+338x^43+524x^44+676x^45+612x^46+502x^47+471x^48+312x^49+121x^50+86x^51+64x^52+36x^53+4x^54+2x^55+12x^56+2x^57+4x^58+1x^66

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 0.266 seconds.