The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+108x^40+136x^41+392x^42+326x^43+835x^44+684x^45+780x^46+258x^47+265x^48+76x^49+133x^50+38x^51+39x^52+16x^53+6x^54+2x^55+1x^74

The gray image is a code over GF(2) with n=360, k=12 and d=160.
This code was found by Heurico 1.16 in 0.25 seconds.