The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^45+962x^46+1744x^47+2778x^48+3636x^49+4801x^50+4808x^51+4994x^52+3592x^53+2726x^54+1268x^55+723x^56+372x^57+149x^58+48x^59+16x^60+12x^61+2x^62+4x^63

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 7.89 seconds.