The generator matrix

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

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+499x^48+872x^49+636x^50+648x^51+412x^52+368x^53+268x^54+168x^55+116x^56+56x^57+45x^58+4x^60+2x^62+1x^66

The gray image is a code over GF(2) with n=408, k=12 and d=192.
This code was found by Heurico 1.16 in 10.1 seconds.