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

generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+504x^245+564x^246+252x^247+21x^248+468x^249+588x^250+144x^251+18x^252+312x^253+192x^254+72x^255+144x^257+156x^258+60x^259+6x^260+108x^261+60x^262+12x^263+6x^264+120x^265+120x^266+12x^267+9x^268+36x^269+24x^270+24x^271+36x^273+24x^274+3x^276

The gray image is a linear code over GF(4) with n=336, k=6 and d=245.
This code was found by Heurico 1.16 in 65 seconds.