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  1  1  1  1  1  1  1  X  1  1  1  1  0  1  1  1  X  1  1  0
 0  X  0 3X+2 2X+2 X+2  2  X 3X 2X  0 3X+2  2  2 X+2  X 3X+2 3X+2  0 3X 2X+2 3X  2 2X+2 2X+2 3X+2 3X  2  0 3X+2  X  0 2X 2X 3X+2 X+2  2 2X+2 2X+2 X+2  X 3X X+2 X+2 2X  X
 0  0  2  0 2X+2 2X+2  0 2X+2 2X 2X+2  0  0 2X 2X+2 2X+2  2 2X  2 2X  2 2X+2  0 2X  0 2X+2  0  0  2 2X+2  2 2X+2 2X  0  2 2X+2 2X 2X  0 2X  2 2X 2X  2  2  2  0
 0  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0  0  0  0  0 2X 2X  0  0 2X
 0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0  0  0 2X  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+185x^42+292x^44+256x^45+631x^46+256x^47+243x^48+135x^50+39x^52+9x^54+1x^84

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 3.34 seconds.