The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+502x^43+691x^44+844x^45+544x^46+540x^47+326x^48+340x^49+117x^50+106x^51+45x^52+32x^53+2x^54+4x^55+1x^56+1x^58

The gray image is a code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.16 in 0.203 seconds.