The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+308x^49+158x^50+260x^51+61x^52+104x^53+33x^54+84x^55+1x^56+12x^57+1x^70+1x^76

The gray image is a code over GF(2) with n=408, k=10 and d=196.
This code was found by Heurico 1.16 in 104 seconds.