The generator matrix

 1  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  X  1  1  1  X  1  X  1  1  X  X  X 2X  1  1  1
 0  X  0  X 2X  0 3X  X  2 X+2  2 3X+2 2X+2  2 X+2 X+2  0 3X X+2  2 X+2  X 2X 3X  0 2X+2 3X  2  X  X  2 X+2  0 3X+2 3X+2 3X+2 2X 2X+2 2X 2X  X  X 2X+2  X 2X+2
 0  0  X  X  2 X+2 X+2  2  2 2X  X 3X  0 X+2 3X+2 2X+2  0 3X+2  2 2X 2X 2X+2  X 3X+2  2  2 2X 3X  X 3X X+2  X X+2 2X+2 3X+2  0 3X+2 2X+2 3X+2  X 2X+2  2  0  2 X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  0  0  0  0  0 2X 2X 2X  0  0 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+96x^41+174x^42+258x^43+349x^44+404x^45+342x^46+148x^47+125x^48+56x^49+27x^50+58x^51+5x^52+4x^53+1x^74

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 0.109 seconds.