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

generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 209.

Homogenous weight enumerator: w(x)=1x^0+432x^209+564x^210+276x^211+9x^212+516x^213+540x^214+132x^215+24x^216+312x^217+228x^218+60x^219+24x^220+156x^221+156x^222+36x^223+204x^225+120x^226+36x^227+48x^229+72x^230+3x^232+60x^233+48x^234+36x^235+3x^252

The gray image is a linear code over GF(4) with n=288, k=6 and d=209.
This code was found by Heurico 1.16 in 15 seconds.