The generator matrix

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

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+444x^241+372x^242+408x^243+771x^244+2004x^245+1188x^246+1044x^247+1806x^248+3108x^249+2064x^250+1560x^251+2637x^252+4224x^253+2316x^254+2016x^255+2244x^256+4632x^257+2016x^258+1992x^259+2580x^260+4188x^261+2304x^262+1500x^263+2244x^264+3768x^265+2004x^266+1296x^267+1605x^268+2328x^269+1104x^270+672x^271+657x^272+1068x^273+408x^274+216x^275+279x^276+312x^277+48x^278+48x^279+24x^280+36x^281

The gray image is a linear code over GF(4) with n=344, k=8 and d=241.
This code was found by Heurico 1.16 in 27.2 seconds.