The generator matrix

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

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+160x^41+59x^42+266x^43+329x^44+456x^45+338x^46+260x^47+20x^48+96x^49+15x^50+34x^51+1x^52+8x^53+4x^54+1x^80

The gray image is a code over GF(2) with n=360, k=11 and d=164.
This code was found by Heurico 1.16 in 3.88 seconds.