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

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+199x^42+410x^43+330x^44+334x^45+247x^46+286x^47+120x^48+50x^49+48x^50+8x^51+12x^52+1x^54+1x^56+1x^66

The gray image is a code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.