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

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

Homogenous weight enumerator: w(x)=1x^0+92x^42+24x^43+120x^44+592x^45+92x^46+24x^47+47x^48+24x^50+7x^52+1x^84

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 107 seconds.