The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  1  0  1  2  1  X  X  1  X  1  X  1  1  1 X^2  1  X  1  2  1  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+2 X^2+X+2  X X^2+2  X X^2+X+2 X+2 X^2 X+2  X  0 X^2+2 X^2+X  X X^2+X  X  2  X X^2 X^2 X^2+X  0 X^2  2 X^2+X+2  X  2 X^2+X X^2+X X^2+2  X X^2+X X^2
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2  X X^2  X X^2+X+2 X^2+X+2 X+2  0  2 X^2+X+2  2  X X^2  2 X^2 X^2 X^2 X^2+X+2  2  X X^2+X  X  0  X X^2+X  0 X^2+X+2  X X^2+X+2 X^2+X  X X^2+2 X+2  0
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0 X^2+2  0  2 X^2  0 X^2 X^2 X^2+2  0  0  2  2  2 X^2+2  2  2 X^2+2 X^2  0  2 X^2  2 X^2+2  2 X^2+2  2 X^2 X^2+2  2  0 X^2  2 X^2

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+80x^41+265x^42+302x^43+542x^44+494x^45+879x^46+466x^47+507x^48+176x^49+155x^50+122x^51+70x^52+14x^53+8x^54+6x^55+4x^57+4x^58+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.