The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+242x^48+454x^49+233x^50+244x^51+224x^52+402x^53+212x^54+8x^55+12x^57+9x^58+5x^60+1x^62+1x^82

The gray image is a code over GF(2) with n=408, k=11 and d=192.
This code was found by Heurico 1.16 in 0.109 seconds.