The generator matrix

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

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+125x^46+238x^47+382x^48+394x^49+692x^50+584x^51+649x^52+380x^53+302x^54+126x^55+85x^56+50x^57+48x^58+12x^59+19x^60+8x^61+1x^78

The gray image is a code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.313 seconds.