The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+314x^46+772x^47+1759x^48+1924x^49+2606x^50+2252x^51+2333x^52+1620x^53+1444x^54+752x^55+391x^56+80x^57+74x^58+16x^59+27x^60+8x^61+10x^62+1x^64

The gray image is a code over GF(2) with n=408, k=14 and d=184.
This code was found by Heurico 1.16 in 2.03 seconds.