The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 X 1 aX 1 1 1 1 (a+1)X 1 1 1 1 aX 1 1 1 1 1 1 1 1 X aX aX (a+1)X X X 1 1 1 1 0 1 1 X 1 1 1 1 1 1 1 1 1 aX 1 1 aX X 1 1 aX 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 X aX (a+1)X X (a+1)X aX aX X 0 (a+1)X+a+1 (a+1)X+a 1 1 1 a+1 X+1 X+1 aX+1 1 aX+a aX+a+1 a 1 1 a X+a+1 aX+1 0 aX+a+1 aX+a X+a+1 a 1 1 1 0 1 1 (a+1)X+1 (a+1)X+1 (a+1)X+a aX+a 1 aX+a (a+1)X+a 1 (a+1)X+1 a (a+1)X+1 (a+1)X 1 0 X+1 1 a 1 (a+1)X+a+1 (a+1)X+a 1 1 (a+1)X+1 aX+a+1 1 a+1 (a+1)X+a aX+1 (a+1)X+a (a+1)X+1 1 X+1 X X+1 1 X a+1 (a+1)X+1 (a+1)X+a+1 aX 0 0 1 0 (a+1)X+1 (a+1)X (a+1)X a 0 aX+1 X+1 X+1 aX+a+1 (a+1)X+a+1 aX+a X+1 X+a (a+1)X 1 X+1 aX (a+1)X+a+1 aX X+a+1 aX+a aX+a+1 a+1 aX+a 0 (a+1)X+a+1 X+a+1 X+a X+1 (a+1)X (a+1)X+a (a+1)X+a a+1 (a+1)X+a+1 (a+1)X+a 1 X aX+1 0 X+a+1 a (a+1)X+1 a 1 aX aX (a+1)X+1 X+1 aX aX+a+1 (a+1)X+a a+1 aX+1 a (a+1)X+a+1 X+1 a+1 X+1 1 (a+1)X+1 X (a+1)X aX+a+1 (a+1)X+a+1 0 1 (a+1)X a aX+a a+1 X+a 1 a a aX aX+1 (a+1)X+a 0 0 0 0 1 a+1 1 a X+a+1 aX+a+1 (a+1)X+a (a+1)X+1 (a+1)X aX+1 (a+1)X+a+1 X+1 (a+1)X+a aX+a (a+1)X+a+1 X aX+1 1 X+a+1 1 (a+1)X+a+1 (a+1)X+a+1 X aX+1 aX aX+a 0 0 (a+1)X (a+1)X+a 0 X+1 (a+1)X X+1 (a+1)X a+1 a+1 X+a a+1 a+1 (a+1)X+a aX+a X+a+1 (a+1)X+a X+a (a+1)X+a+1 aX+a+1 a X+1 X aX+a (a+1)X+a+1 X a+1 (a+1)X+1 aX+1 1 1 0 X (a+1)X+a aX+a+1 0 aX+a+1 X+a X aX+1 X+1 X 1 X X+1 (a+1)X+a (a+1)X 1 (a+1)X+a (a+1)X+a+1 0 aX generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 229. Homogenous weight enumerator: w(x)=1x^0+204x^229+420x^230+276x^231+1020x^232+1644x^233+1596x^234+1224x^235+1944x^236+2676x^237+2088x^238+1320x^239+3063x^240+3204x^241+2724x^242+1476x^243+2877x^244+3924x^245+3084x^246+1452x^247+3327x^248+4104x^249+2844x^250+1416x^251+2757x^252+2736x^253+2388x^254+1152x^255+1875x^256+2076x^257+1296x^258+756x^259+759x^260+816x^261+420x^262+120x^263+255x^264+108x^265+36x^266+24x^267+39x^268+12x^269+3x^272 The gray image is a linear code over GF(4) with n=328, k=8 and d=229. This code was found by Heurico 1.16 in 23.6 seconds.