The generator matrix

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

generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+297x^208+276x^209+240x^210+168x^211+603x^212+372x^213+288x^214+84x^215+240x^216+180x^217+48x^218+60x^219+306x^220+168x^221+84x^222+36x^223+171x^224+60x^225+36x^226+12x^227+111x^228+36x^229+60x^230+24x^231+48x^232+60x^233+12x^234+12x^236+3x^240

The gray image is a linear code over GF(4) with n=288, k=6 and d=208.
This code was found by Heurico 1.16 in 0.103 seconds.