The generator matrix

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

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+80x^42+198x^43+247x^44+370x^45+366x^46+376x^47+165x^48+88x^49+50x^50+38x^51+50x^52+14x^53+4x^55+1x^76

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 0.125 seconds.