The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1 X^2  1  1  1 X^2+2  1  1  1  1  X  1  1  0  X  1  1  1  1  1  1 X^2  2  1  0  1  1  1 X^2+X+2  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1 X^2+1  2 X+2  1 X^2+1 X^2+X+2 X^2+X+3 X+1  1 X+1  1  1  1 X+3 X^2+1  1 X^2+X+3 X^2+X+3  X  1  1 X^2  1 X+2 X^2+X+2 X^2+2  1 X^2+2 X^2+3
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2+X+2 X^2+2 X^2+X X^2+X+2  0 X^2  2 X^2+X+2 X^2+X+2 X^2 X^2+X X^2+X  0  X X+2 X^2 X^2 X^2+X+2 X^2  2  X X^2 X^2+2 X+2  0  X X+2  2 X^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+134x^43+592x^44+270x^45+161x^46+242x^47+482x^48+102x^49+13x^50+8x^51+28x^52+12x^53+1x^58+1x^62+1x^64

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 0.078 seconds.