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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 246.

Homogenous weight enumerator: w(x)=1x^0+192x^246+36x^248+24x^252+3x^256

The gray image is a linear code over GF(4) with n=328, k=4 and d=246.
This code was found by Heurico 1.16 in 0.331 seconds.