The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0 a*X a*X a^2*X a^2*X a^2*X a^2*X  X  X a^2*X  0  X a*X  0  0 a*X  X  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X  X  0 a*X  X  X  X  X  X  0 a^2*X  X  0 a^2*X a*X  0 a^2*X  0
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X  0 a*X a^2*X  0 a^2*X  0  X a^2*X  X  X a*X  0 a*X a*X  0 a^2*X  X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X a*X  0  X  X  X  0  X a^2*X a*X  0  X  X a*X a^2*X a*X a*X a^2*X

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+72x^136+219x^140+195x^144+768x^147+141x^148+2304x^151+90x^152+66x^156+66x^160+36x^164+48x^168+57x^172+24x^176+6x^180+3x^196

The gray image is a linear code over GF(4) with n=200, k=6 and d=136.
This code was found by Heurico 1.16 in 0.151 seconds.