The generator matrix

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

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+359x^42+208x^43+328x^44+256x^45+426x^46+144x^47+245x^48+32x^49+43x^50+4x^54+1x^60+1x^68

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 30.4 seconds.