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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+924x^248+1344x^252+885x^256+360x^260+252x^264+96x^268+111x^272+120x^276+3x^304

The gray image is a linear code over GF(4) with n=340, k=6 and d=248.
This code was found by Heurico 1.16 in 8.28 seconds.