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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+210x^200+201x^204+615x^208+1413x^212+1398x^216+45x^220+42x^224+24x^228+39x^232+27x^236+45x^240+15x^244+9x^248+3x^252+6x^256+3x^272

The gray image is a linear code over GF(4) with n=284, k=6 and d=200.
This code was found by Heurico 1.16 in 63.4 seconds.