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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+198x^200+24x^204+21x^208+12x^216

The gray image is a linear code over GF(4) with n=268, k=4 and d=200.
This code was found by Heurico 1.16 in 0.265 seconds.