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 X aX 1 1 1 1 0 1 1 X 1 1 1 0 1 1 aX 1 1 1 X 0 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 0 a+1 (a+1)X (a+1)X+a+1 1 1 (a+1)X+a 1 X+a+1 X+a 1 a+1 (a+1)X+1 1 X X (a+1)X+a+1 1 (a+1)X+a+1 (a+1)X+1 0 aX+1 X+1 a 1 aX X+1 0 X X+1 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 X+1 (a+1)X+a+1 a+1 (a+1)X+a X (a+1)X+a+1 aX+a+1 (a+1)X+a+1 aX+a+1 aX+a X+a (a+1)X+1 1 aX+a aX+a a+1 aX X 0 (a+1)X+1 1 a X+a+1 aX+a+1 (a+1)X 1 (a+1)X (a+1)X (a+1)X+1 X+1 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+a+1 X a a (a+1)X+a a (a+1)X+a+1 X+a X+a+1 (a+1)X+a a a a 0 0 (a+1)X+1 X+1 X+1 (a+1)X+a 1 aX+a aX+a+1 1 aX aX (a+1)X+a+1 (a+1)X+a+1 (a+1)X+1 X+1 X+a generates a code of length 78 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 218. Homogenous weight enumerator: w(x)=1x^0+420x^218+672x^219+1014x^220+540x^221+1788x^222+1632x^223+2433x^224+996x^225+2448x^226+2508x^227+3570x^228+1284x^229+3336x^230+3000x^231+3603x^232+1464x^233+3708x^234+3024x^235+3471x^236+1296x^237+3612x^238+2508x^239+3402x^240+1080x^241+2808x^242+2112x^243+2424x^244+744x^245+1392x^246+1140x^247+891x^248+252x^249+408x^250+276x^251+177x^252+24x^253+48x^254+24x^255+6x^256 The gray image is a linear code over GF(4) with n=312, k=8 and d=218. This code was found by Heurico 1.16 in 24.3 seconds.