The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 X 1 1 1 1 (a+1)X 1 X 1 0 1 1 1 1 (a+1)X aX 1 1 (a+1)X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 (a+1)X 1 1 1 1 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 (a+1)X+a+1 1 (a+1)X+1 a aX+a+1 0 aX+1 1 a (a+1)X+a+1 aX+1 (a+1)X+a+1 0 X+a aX+a+1 (a+1)X 1 1 (a+1)X+1 a 1 aX+a X aX+a+1 aX 1 X+1 1 (a+1)X+a 1 a+1 X+1 X+a+1 X+a 1 1 aX+a+1 (a+1)X+a 1 (a+1)X+a 1 1 1 1 (a+1)X+1 (a+1)X+a aX X+1 (a+1)X+a (a+1)X+a a+1 (a+1)X+a+1 a+1 X+a (a+1)X+a (a+1)X+a (a+1)X 1 aX 1 1 (a+1)X+a aX 1 aX+1 aX+a X+1 0 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 aX (a+1)X (a+1)X (a+1)X aX X aX X aX (a+1)X X X aX aX (a+1)X aX (a+1)X aX (a+1)X aX aX 0 X (a+1)X (a+1)X 0 0 aX X aX (a+1)X 0 0 X aX 0 aX aX 0 (a+1)X 0 (a+1)X aX (a+1)X X (a+1)X (a+1)X 0 (a+1)X (a+1)X X (a+1)X aX aX X 0 X aX 0 aX 0 0 0 0 0 0 X 0 X (a+1)X (a+1)X X (a+1)X 0 (a+1)X X X 0 X (a+1)X 0 (a+1)X 0 0 X (a+1)X (a+1)X X aX (a+1)X (a+1)X X (a+1)X (a+1)X 0 0 X aX 0 (a+1)X X X (a+1)X 0 (a+1)X (a+1)X X 0 (a+1)X aX 0 (a+1)X X (a+1)X 0 aX X 0 (a+1)X (a+1)X X aX X X (a+1)X 0 X X aX (a+1)X aX 0 aX (a+1)X X aX 0 0 0 0 aX (a+1)X aX X 0 (a+1)X 0 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 X (a+1)X X aX X (a+1)X 0 (a+1)X aX X 0 0 X aX (a+1)X (a+1)X aX (a+1)X (a+1)X 0 aX X aX X X 0 aX 0 (a+1)X 0 (a+1)X 0 X (a+1)X X aX 0 X 0 0 0 aX 0 aX aX aX 0 X 0 aX aX aX X aX 0 X X 0 aX X (a+1)X X (a+1)X (a+1)X 0 0 (a+1)X X generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 236. Homogenous weight enumerator: w(x)=1x^0+159x^236+72x^238+312x^239+831x^240+324x^242+780x^243+1050x^244+468x^246+960x^247+990x^248+696x^250+1284x^251+1188x^252+528x^254+1272x^255+1185x^256+660x^258+948x^259+996x^260+276x^262+528x^263+411x^264+48x^266+60x^267+201x^268+57x^272+27x^276+24x^280+9x^284+18x^288+15x^292+3x^296+3x^300 The gray image is a linear code over GF(4) with n=336, k=7 and d=236. This code was found by Heurico 1.16 in 1.97 seconds.