The generator matrix

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

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+294x^200+516x^201+600x^202+684x^203+1662x^204+2088x^205+1860x^206+1452x^207+2397x^208+2916x^209+2424x^210+1764x^211+3375x^212+3552x^213+2640x^214+1896x^215+3759x^216+3540x^217+2880x^218+2100x^219+3525x^220+3696x^221+2868x^222+1584x^223+2850x^224+2208x^225+1416x^226+960x^227+1260x^228+1236x^229+600x^230+300x^231+291x^232+180x^233+72x^234+12x^235+39x^236+36x^237+3x^244

The gray image is a linear code over GF(4) with n=288, k=8 and d=200.
This code was found by Heurico 1.16 in 22 seconds.