The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+258x^43+316x^44+380x^45+317x^46+274x^47+221x^48+184x^49+17x^50+38x^51+21x^52+12x^53+6x^55+1x^58+1x^60+1x^62

The gray image is a code over GF(2) with n=368, k=11 and d=172.
This code was found by Heurico 1.16 in 30.3 seconds.