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

generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+1008x^236+1323x^240+732x^244+336x^248+324x^252+189x^256+96x^260+84x^264+3x^272

The gray image is a linear code over GF(4) with n=324, k=6 and d=236.
This code was found by Heurico 1.16 in 0.172 seconds.