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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 239.

Homogenous weight enumerator: w(x)=1x^0+708x^239+288x^240+1068x^243+402x^244+504x^247+132x^248+348x^251+72x^252+168x^255+27x^256+120x^259+36x^260+108x^263+48x^264+48x^267+12x^268+6x^276

The gray image is a linear code over GF(4) with n=328, k=6 and d=239.
This code was found by Heurico 1.16 in 0.312 seconds.