The generator matrix

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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+72x^245+144x^246+3x^248+24x^249+6x^264+6x^268

The gray image is a linear code over GF(4) with n=328, k=4 and d=245.
This code was found by Heurico 1.16 in 0.093 seconds.