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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  0  1  1  1  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X X^2+X  2  0 X+2 X^2 X^2+X X^2  X  0 X^2+X X^2 X+2  0 X^2+X+2  0 X^2+X  2  X X^2+2  X X^2 X^2+X X^2+X  0  X X^2+2 X^2+X+2  2 X^2+2  X X^2+X+2 X^2+X X^2+X+2 X^2 X^2+X  X X^2+2 X^2+2  X X^2 X^2+2 X+2 X^2+X
 0  0 X^2+2  0 X^2 X^2  0 X^2  0 X^2  2 X^2 X^2 X^2+2  0  2  0  2 X^2+2 X^2+2 X^2+2 X^2  2  2  0 X^2 X^2+2  0  0 X^2  2 X^2  0  0  0  2 X^2+2 X^2  2  0 X^2+2 X^2 X^2+2 X^2  2  2  2 X^2 X^2 X^2+2  0
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  2  0  0  0  2  0  2  0  0  2  0  2  2  0
 0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0  0  0  2  0  0  0  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+232x^47+22x^48+88x^49+376x^50+656x^51+344x^52+64x^53+8x^54+232x^55+16x^56+8x^57+1x^96

The gray image is a code over GF(2) with n=408, k=11 and d=188.
This code was found by Heurico 1.16 in 78.8 seconds.