The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+80x^39+593x^40+1544x^41+2784x^42+3918x^43+4864x^44+5208x^45+5311x^46+3800x^47+2399x^48+1328x^49+574x^50+214x^51+93x^52+32x^53+19x^54+4x^55+1x^56+1x^60

The gray image is a code over GF(2) with n=360, k=15 and d=156.
This code was found by Heurico 1.16 in 6.78 seconds.