The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+364x^47+1013x^48+1140x^49+1142x^50+1452x^51+1011x^52+788x^53+476x^54+380x^55+253x^56+84x^57+62x^58+12x^59+9x^60+4x^61+1x^64

The gray image is a code over GF(2) with n=408, k=13 and d=188.
This code was found by Heurico 1.16 in 0.515 seconds.