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

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+32x^42+48x^43+65x^44+224x^45+61x^46+48x^47+28x^48+2x^50+1x^52+1x^54+1x^80

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 0.063 seconds.