The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+276x^42+900x^43+1189x^44+1492x^45+1182x^46+1128x^47+733x^48+572x^49+374x^50+240x^51+65x^52+16x^53+14x^54+4x^55+4x^56+2x^58

The gray image is a code over GF(2) with n=368, k=13 and d=168.
This code was found by Heurico 1.16 in 0.453 seconds.