The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 (a+1)X 1 1 1 1 (a+1)X (a+1)X 1 (a+1)X 1 1 1 1 X 1 1 1 1 X 1 1 aX 1 X 1 1 1 1 X 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 aX 1 1 1 1 1 1 1 1 1 aX 1 1 1 1 (a+1)X 1 1 0 1 aX 1 1 1 1 1 1 1 1 0 1 0 0 0 (a+1)X 1 (a+1)X+a a+1 (a+1)X+1 1 (a+1)X+a (a+1)X+a+1 (a+1)X+a+1 1 1 a (a+1)X+1 a+1 X+a 1 1 (a+1)X+a+1 (a+1)X aX+1 aX+a 0 X 1 a X+1 aX a+1 1 a+1 (a+1)X 1 aX+a+1 1 aX+1 a a X+a 1 X+a aX+a+1 a aX aX+a+1 (a+1)X+1 X+a+1 X+1 0 1 a+1 X+a+1 aX+1 1 X+1 (a+1)X (a+1)X aX+1 X+a X X a+1 aX+1 1 X+a+1 X+a a+1 aX+a+1 1 X+a 1 1 X+a+1 1 aX+a+1 X aX+a a+1 (a+1)X+1 aX+a+1 (a+1)X (a+1)X+1 0 0 1 1 a a+1 1 X+1 1 0 a+1 X+a+1 aX a a 1 aX+a a a+1 aX a+1 a+1 (a+1)X+a 1 (a+1)X+a+1 aX+a X+1 aX+a+1 0 a+1 (a+1)X+a 0 (a+1)X+a+1 aX+1 X+1 a aX+a aX (a+1)X+a+1 (a+1)X+1 aX+a X+1 (a+1)X+1 X+a 0 a (a+1)X+1 X+1 a+1 (a+1)X (a+1)X+1 aX+a X+a+1 0 aX+1 X X aX+1 X+a+1 X aX+a (a+1)X+1 1 0 X (a+1)X+1 (a+1)X aX+1 (a+1)X+a (a+1)X (a+1)X+a+1 a aX (a+1)X 1 a+1 (a+1)X+a 1 0 aX+a 1 (a+1)X+a+1 aX+1 X+a a+1 X+a 0 0 0 (a+1)X 0 0 0 aX aX aX (a+1)X X X X X (a+1)X (a+1)X aX (a+1)X aX aX 0 0 (a+1)X X X aX (a+1)X (a+1)X X 0 0 0 aX 0 aX X (a+1)X 0 (a+1)X aX X (a+1)X 0 (a+1)X X 0 (a+1)X X 0 0 X (a+1)X 0 X aX (a+1)X aX aX (a+1)X 0 X 0 X X 0 aX aX 0 (a+1)X X X (a+1)X 0 X X (a+1)X X aX X aX 0 aX 0 aX (a+1)X 0 0 0 0 X aX (a+1)X X 0 aX X (a+1)X X 0 X (a+1)X aX 0 aX aX 0 0 X 0 aX X (a+1)X X aX X 0 aX (a+1)X X 0 aX aX aX aX (a+1)X (a+1)X 0 aX (a+1)X 0 (a+1)X 0 (a+1)X aX (a+1)X X aX (a+1)X X aX X aX 0 X 0 0 (a+1)X X aX 0 aX X aX aX X (a+1)X X X 0 0 aX 0 aX 0 (a+1)X aX X 0 X X X generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 240. Homogenous weight enumerator: w(x)=1x^0+186x^240+444x^241+192x^242+780x^243+1155x^244+1548x^245+768x^246+1428x^247+2172x^248+2772x^249+1200x^250+2004x^251+2664x^252+3336x^253+1524x^254+2832x^255+3471x^256+3600x^257+1680x^258+2832x^259+3438x^260+3432x^261+1788x^262+2280x^263+3294x^264+3276x^265+1200x^266+1860x^267+1899x^268+1944x^269+684x^270+1008x^271+912x^272+924x^273+144x^274+300x^275+153x^276+204x^277+36x^278+36x^279+39x^280+24x^281+21x^284+6x^288+24x^292+9x^296+6x^300+6x^304 The gray image is a linear code over GF(4) with n=344, k=8 and d=240. This code was found by Heurico 1.16 in 28.2 seconds.