The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+276x^46+908x^47+1548x^48+2220x^49+2202x^50+2504x^51+2177x^52+2044x^53+1104x^54+748x^55+408x^56+116x^57+54x^58+32x^59+29x^60+4x^61+4x^62+5x^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 1.94 seconds.