The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^49+105x^50+12x^51+10x^52+24x^53+38x^54+4x^55+5x^56+6x^57+1x^58

The gray image is a code over GF(2) with n=408, k=8 and d=196.
This code was found by Heurico 1.16 in 0.172 seconds.