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

generates a code of length 72 over F4[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+75x^200+168x^204+48x^207+162x^208+432x^211+162x^212+1296x^215+105x^216+1296x^219+87x^220+54x^224+42x^228+54x^232+30x^236+21x^240+24x^244+21x^248+9x^252+3x^260+3x^264+3x^276

The gray image is a linear code over GF(4) with n=288, k=6 and d=200.
This code was found by Heurico 1.16 in 0.257 seconds.