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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+70x^41+69x^42+78x^43+18x^44+300x^45+984x^46+300x^47+7x^48+78x^49+66x^50+70x^51+6x^52+1x^90

The gray image is a code over GF(2) with n=368, k=11 and d=164.
This code was found by Heurico 1.16 in 0.234 seconds.