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  1  1  X  1  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X+2 X^2  0 X^2+X+2 X^2+X+2  X X^2+2 X^2 X^2+X+2 X^2+X+2 X+2 X^2 X^2+2  2  2 X^2+X X^2+X  2 X^2+2 X^2  X  2 X+2  0 X^2+X  2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X+2  0  2 X+2 X^2+X X^2 X^2+X X^2 X^2+X+2  0  X X^2+2 X+2 X+2  2 X^2+2  0 X^2+X X^2+X X^2+X+2  0 X^2+X+2 X+2 X^2+X+2 X^2 X+2 X^2+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+70x^42+72x^43+141x^44+470x^45+137x^46+60x^47+57x^48+6x^49+9x^50+1x^88

The gray image is a code over GF(2) with n=360, k=10 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.