The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+174x^41+405x^42+604x^43+627x^44+546x^45+687x^46+552x^47+264x^48+138x^49+39x^50+26x^51+19x^52+2x^53+2x^54+4x^57+2x^58+2x^59+1x^62+1x^64

The gray image is a code over GF(2) with n=360, k=12 and d=164.
This code was found by Heurico 1.16 in 99.1 seconds.