The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^42+72x^43+220x^44+312x^45+510x^46+312x^47+190x^48+72x^49+158x^50+16x^52+2x^54+4x^56+1x^80

The gray image is a code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 2.2 seconds.