The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+388x^47+873x^48+1284x^49+1262x^50+1268x^51+1026x^52+716x^53+592x^54+404x^55+194x^56+124x^57+18x^58+36x^59+4x^61+2x^68

The gray image is a code over GF(2) with n=408, k=13 and d=188.
This code was found by Heurico 1.16 in 0.547 seconds.