The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  X  1  1 a*X  1  1  1  1  1  0  1  1 a*X  1  1  1  1 a^2*X  1  1  1 a^2*X  1  1  1  1  1  1  X a*X a*X  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  X a*X  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2  X a^2*X+a^2 X+a a^2*X+1  1 a^2*X+a^2  a  1  0 a*X+a a*X+a^2 a^2*X+1 a*X+1  1 a^2*X a*X+1  1 X+a  0 a*X+1 a*X+a^2  1 a*X+a a*X+1 a*X+1  1 X+a^2 a^2 X+1 a^2*X X+a^2 X+a^2  1  1  1 X+1 a*X+a^2 a^2*X+1  X a*X  1 X+a  1 a^2 a*X+a a^2*X+a a^2*X  X a^2*X+1  X  X a^2*X a*X+a^2  1  1 a*X+a^2  0
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X  X a*X a^2*X a^2*X  0 a^2*X a^2*X a*X a^2*X a*X  0 a*X  X  X a^2*X a*X a^2*X  0 a^2*X  0 a*X a*X a*X  X a*X a^2*X a^2*X  X  X  X a^2*X  X  0  X  X a*X a*X a*X a*X a*X a^2*X  X  0  0  X  0  0 a^2*X  0 a*X  X  0 a^2*X a*X  X  0  0
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0 a^2*X  0  0 a*X a*X  X  X a^2*X a^2*X  0 a*X a*X  0 a^2*X  X  X a*X  X  X  X  0 a^2*X  X  0  X  X a*X a*X  X  0 a^2*X  X a*X a*X  0 a*X a*X  0 a*X  X a*X a^2*X a*X  0 a*X a^2*X a*X  0 a*X  0  X a*X a*X a*X  0 a^2*X  0
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X a*X a*X  X a^2*X a^2*X  0 a^2*X a^2*X  X  0 a^2*X  0 a^2*X a^2*X a*X  X  X a*X  X  X a^2*X  0 a*X a*X  0 a*X  0  X  X a*X a*X a^2*X  0  X  0 a*X a*X a*X a^2*X  X a*X  X  X  0 a*X  0 a^2*X a*X a*X  0  0  X a^2*X a*X a*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+162x^200+552x^203+405x^204+1524x^207+603x^208+2004x^211+555x^212+2424x^215+666x^216+2736x^219+777x^220+2244x^223+429x^224+660x^227+303x^228+144x^231+63x^232+39x^236+36x^240+15x^244+21x^248+15x^252+3x^256+3x^260

The gray image is a linear code over GF(4) with n=288, k=7 and d=200.
This code was found by Heurico 1.16 in 1.64 seconds.