The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  0 X^2 X^2+X+2  1  1  1  X X^2+X+2  2  1 X+2  1 X+2  1  1  1  X  1 X^2  0 X^2+2  1  1 X^2+X+2  1  1 X^2+X+2  1 X^2+X X^2+2  1  X X^2  1  2  1  1  1 X^2+2  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  3  1  X  1 X^2+X X^2+X+2 X+1  1  1  1 X^2+X+3  0 X+3  1 X^2 X+1 X+2  X X^2+X+2  1 X^2  1  0  1 X^2 X+2 X^2+X+3  X  3  1  1  2  1  1 X+2  1  X X^2+2 X^2+X+3  1  0
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X+2  X  1 X^2+3 X^2+3 X^2+X X+1  X X^2+X+1 X^2+1 X+2  1  2 X^2 X^2+X+2  1 X+3  1  0  0  1 X^2+X+3 X^2 X^2+1  1 X^2+X+3 X^2+X  1 X^2+2  1  3 X^2+1  0 X+1 X^2 X^2+X+2  X X^2 X+3 X+2  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+86x^47+516x^48+582x^49+790x^50+700x^51+454x^52+316x^53+284x^54+94x^55+156x^56+66x^57+28x^58+8x^59+8x^60+4x^61+2x^62+1x^64

The gray image is a code over GF(2) with n=408, k=12 and d=188.
This code was found by Heurico 1.16 in 0.14 seconds.