The generator matrix

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

generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+399x^196+852x^197+816x^198+1056x^199+2580x^200+2916x^201+2472x^202+2724x^203+5313x^204+5376x^205+4488x^206+4776x^207+9960x^208+9264x^209+7836x^210+7584x^211+13698x^212+13200x^213+10548x^214+9936x^215+17100x^216+15084x^217+12276x^218+10236x^219+16047x^220+13944x^221+9792x^222+8184x^223+12552x^224+8520x^225+5268x^226+3576x^227+4803x^228+3948x^229+1524x^230+912x^231+1356x^232+600x^233+276x^234+168x^235+90x^236+24x^237+33x^240+18x^244+6x^248+12x^256

The gray image is a linear code over GF(4) with n=288, k=9 and d=196.
This code was found by Heurico 1.16 in 296 seconds.