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 X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X+2 X^2+2 X^2+X X^2 X^2+X+2  0 X+2  2  X X^2+2 X^2+X  0 X+2  0 X+2 X^2+X X^2+X+2 X^2+2 X^2+2  2 X^2+X+2 X^2 X+2  0  2 X^2+X X^2+X X^2 X^2 X+2 X^2+X X+2  X X^2+2 X^2+2 X^2+2 X^2+X
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  2  2  0  2  2  2  0  0  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  2
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  0  2  0  2  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2  2  2  0  0  0  2  2  0  2  2  0  0  0  2  0  0  2  2  0  0  0  2  2

generates a code of length 46 over Z4[X]/(X^3+2,2X) 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.