The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1 aX aX  0  0 (a+1)X  1  1  1  1  1  1 (a+1)X  1  0  1  1  1 aX  1  1  1  1  1  1  1  1  1 aX  1  1  X  1  0  1  1  1  1 (a+1)X  1  1  1 aX  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0 (a+1)X  0 (a+1)X  1 (a+1)X+a (a+1)X+1 aX+1 aX+1 aX+a+1  a aX a+1 X+a+1 X+a  1  1  1  1  1  1 aX+a+1 aX+1 aX+a  1 (a+1)X  a  1 (a+1)X+1 (a+1)X a+1  0 (a+1)X  1  1 a+1 (a+1)X+a+1 X+a+1 aX+a aX  0 X+a (a+1)X+a+1  1 X+a  0  1 (a+1)X+1  1  X  0  a X+a+1 aX (a+1)X+a+1  X a+1  1 (a+1)X+a  1  X aX+1 aX+a+1 (a+1)X+1  X  0  a (a+1)X+1 aX
 0  0  1  0  X aX  0 (a+1)X (a+1)X aX aX (a+1)X  X (a+1)X+a+1  1 (a+1)X+1  a (a+1)X+a  1  a (a+1)X+a X+a+1 X+1 X+1 (a+1)X+a aX+a+1 aX+a X+a X+a a+1  a aX+1  1 aX+a+1 aX+a aX+a a+1 aX+a+1 (a+1)X+a X+1 X+1 aX+a+1 aX+1 a+1 aX+a aX X+a+1  0 (a+1)X+1 X+a+1 (a+1)X+1 (a+1)X+1 X+1 (a+1)X+a  0 a+1  1  a X+a+1 X+1 (a+1)X+1 aX+1 (a+1)X+1 a+1 X+a+1  X  a aX aX+a+1 (a+1)X aX+a  a
 0  0  0  1 (a+1)X+1  a a+1 (a+1)X+a+1 X+a+1 aX+a (a+1)X aX+1 X+a (a+1)X+a X+a+1 aX+a+1 aX+a+1  0 aX+a aX+1 X+a  1 aX+a+1  a  X a+1 X+a+1 X+a+1 (a+1)X aX aX  1  a aX+a (a+1)X+a aX+1  0 X+a (a+1)X+a aX+a  0 X+1 aX+a+1  1 aX+a aX+1 aX+a  X aX (a+1)X+a+1  0 (a+1)X+1  a aX+a+1 (a+1)X+1 X+1 X+a X+1 (a+1)X+a (a+1)X+1 aX+a+1 X+1 a+1 aX  a (a+1)X+a+1 X+a  0 (a+1)X+a+1  a (a+1)X+1 a+1

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

Homogenous weight enumerator: w(x)=1x^0+435x^200+360x^201+468x^202+1020x^203+2343x^204+1080x^205+1332x^206+1236x^207+3984x^208+1860x^209+2028x^210+2148x^211+4509x^212+2376x^213+2424x^214+2232x^215+5727x^216+2184x^217+2340x^218+2412x^219+5097x^220+2196x^221+1872x^222+1740x^223+4080x^224+1380x^225+1248x^226+1140x^227+1983x^228+672x^229+468x^230+360x^231+474x^232+168x^233+108x^234+36x^236+12x^237+3x^240

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 21.8 seconds.