The generator matrix

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

generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+375x^204+468x^205+420x^206+288x^207+1158x^208+816x^209+600x^210+288x^211+1644x^212+984x^213+708x^214+372x^215+1353x^216+816x^217+480x^218+192x^219+1119x^220+792x^221+372x^222+204x^223+816x^224+300x^225+240x^226+132x^227+465x^228+276x^229+228x^230+48x^231+213x^232+132x^233+24x^234+12x^235+18x^236+24x^237+3x^244+3x^256

The gray image is a linear code over GF(4) with n=288, k=7 and d=204.
This code was found by Heurico 1.16 in 1.06 seconds.