The generator matrix

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

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+368x^43+68x^44+176x^45+48x^46+336x^47+8x^48+16x^49+2x^56+1x^64

The gray image is a code over GF(2) with n=360, k=10 and d=172.
This code was found by Heurico 1.16 in 0.062 seconds.