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

generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+1344x^252+1257x^256+684x^260+312x^264+192x^268+99x^272+84x^276+120x^280+3x^304

The gray image is a linear code over GF(4) with n=344, k=6 and d=252.
This code was found by Heurico 1.16 in 28.3 seconds.