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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 242.

Homogenous weight enumerator: w(x)=1x^0+672x^242+432x^243+111x^244+624x^246+528x^247+66x^248+384x^250+264x^251+12x^252+240x^254+156x^255+24x^256+192x^258+48x^259+21x^260+60x^262+72x^263+15x^264+72x^266+24x^267+60x^270+12x^271+3x^272+3x^296

The gray image is a linear code over GF(4) with n=332, k=6 and d=242.
This code was found by Heurico 1.16 in 24.5 seconds.