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

generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+102x^244+324x^245+228x^246+264x^247+336x^248+672x^249+444x^250+168x^251+165x^252+372x^253+144x^254+36x^255+45x^256+132x^257+48x^258+36x^259+75x^260+60x^261+24x^262+36x^263+75x^264+84x^265+12x^266+12x^267+3x^268+36x^269+12x^270+24x^272+48x^273+48x^274+24x^275+3x^284+3x^288

The gray image is a linear code over GF(4) with n=336, k=6 and d=244.
This code was found by Heurico 1.16 in 0.145 seconds.