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

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+81x^128+294x^132+411x^136+48x^138+447x^140+576x^142+411x^144+2592x^146+447x^148+5184x^150+468x^152+3888x^154+381x^156+408x^160+309x^164+225x^168+132x^172+63x^176+6x^180+12x^184

The gray image is a linear code over GF(4) with n=200, k=7 and d=128.
This code was found by Heurico 1.16 in 2.1 seconds.