The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^41+150x^42+200x^43+364x^44+340x^45+404x^46+196x^47+49x^48+112x^49+54x^50+16x^51+4x^53+4x^55+1x^56+1x^72

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 112 seconds.