The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+136x^45+828x^46+1780x^47+2796x^48+3716x^49+4715x^50+4840x^51+5098x^52+3854x^53+2431x^54+1282x^55+741x^56+318x^57+113x^58+64x^59+44x^60+6x^61+1x^62+2x^63+2x^65

The gray image is a code over GF(2) with n=408, k=15 and d=180.
This code was found by Heurico 1.16 in 7.66 seconds.