The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+98x^43+96x^44+180x^45+38x^46+50x^47+22x^48+24x^49+1x^52+1x^54+1x^66

The gray image is a code over GF(2) with n=360, k=9 and d=172.
This code was found by Heurico 1.16 in 0.062 seconds.