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

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

Homogenous weight enumerator: w(x)=1x^0+15x^42+54x^43+147x^44+88x^45+139x^46+48x^47+11x^48+5x^50+2x^51+1x^52+1x^78

The gray image is a code over GF(2) with n=360, k=9 and d=168.
This code was found by Heurico 1.16 in 0.062 seconds.