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  X  1  1  1  1  1  1  1  1  1  1
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  2 3X 2X  X  2 X+2  X  0  2 3X+2 3X+2 2X 2X+2 3X 3X  0 3X+2 3X+2  0  2  2 3X 3X 2X  0 2X 3X+2 X+2 X+2 2X  2 2X+2  0 X+2  X
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X 2X 2X+2  2 2X+2  2 2X+2  0  0  0  2 2X+2 2X+2 2X  2 2X 2X+2 2X  2  2 2X  0  2 2X  0  0  2 2X  0  2 2X+2 2X+2 2X+2 2X+2 2X
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X 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+68x^42+52x^43+66x^44+676x^45+56x^46+28x^47+52x^48+12x^49+12x^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 0.39 seconds.