The generator matrix

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

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+176x^40+786x^41+1539x^42+2184x^43+2257x^44+2776x^45+2311x^46+2068x^47+1143x^48+640x^49+318x^50+92x^51+53x^52+20x^53+7x^54+8x^55+2x^56+2x^57+1x^58

The gray image is a code over GF(2) with n=360, k=14 and d=160.
This code was found by Heurico 1.16 in 1.73 seconds.