The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  2  1  1  1  1  1  X  1  1  1  X  1  0 2X  X 2X  1  2  1 2X  2  1
 0  X  0  X  0 2X X+2  X  2 X+2  2 3X+2  2 2X+2 3X 3X+2 3X  2 2X+2 3X+2 3X+2 3X X+2 2X  2 3X  2  2 3X+2 2X+2 X+2 3X+2 2X  X 3X 2X  0  X  X  X  2  X 2X+2  X  X  0
 0  0  X  X 2X+2 3X+2 X+2  2 2X+2 2X  0 2X+2  X X+2 X+2  X 3X  X  0 2X+2 3X 3X+2  2 3X+2  X  0  2 2X+2 3X+2  X 2X 2X+2 3X 3X X+2  0  X 2X+2  X  X 2X+2 3X+2 3X+2  2  2  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X
 0  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  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+90x^41+227x^42+376x^43+469x^44+584x^45+713x^46+610x^47+420x^48+258x^49+153x^50+84x^51+51x^52+28x^53+10x^54+18x^55+3x^56+1x^70

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 0.25 seconds.