The generator matrix

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

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+188x^47+306x^48+980x^49+460x^50+396x^51+364x^52+944x^53+210x^54+148x^55+32x^56+12x^57+32x^58+20x^59+1x^64+2x^70

The gray image is a code over GF(2) with n=408, k=12 and d=188.
This code was found by Heurico 1.16 in 0.25 seconds.