The generator matrix

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

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+359x^42+208x^43+328x^44+256x^45+426x^46+144x^47+245x^48+32x^49+43x^50+4x^54+1x^60+1x^68

The gray image is a code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.16 in 29.5 seconds.