The generator matrix

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

generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 241.

Homogenous weight enumerator: w(x)=1x^0+72x^241+324x^242+132x^244+408x^245+732x^246+219x^248+516x^249+1260x^250+144x^252+1116x^253+1632x^254+153x^256+1212x^257+1392x^258+93x^260+1260x^261+1464x^262+66x^264+924x^265+1308x^266+48x^268+468x^269+864x^270+39x^272+156x^273+228x^274+30x^276+12x^277+12x^278+21x^280+12x^284+15x^288+9x^292+15x^296+12x^300+12x^304+3x^312

The gray image is a linear code over GF(4) with n=344, k=7 and d=241.
This code was found by Heurico 1.16 in 27.8 seconds.