The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^51+2x^52+12x^53+4x^54+2x^55+1x^56

The gray image is a code over GF(2) with n=408, k=6 and d=204.
This code was found by Heurico 1.16 in 0.078 seconds.