The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 X 1 X 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 1 1 1 a^2*X 1 1 X 0 1 0 1 X 1 1 1 1 1 1 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 0 1 0 0 a^2*X a*X a^2*X X X X 1 1 1 a a^2*X+a^2 a*X+1 X+a a^2*X+1 a^2*X+a X+a^2 1 X+a^2 1 1 0 a*X+a^2 1 a*X+a a^2*X X+1 a*X+1 a*X+1 X+a a^2*X+a^2 a^2*X+a 0 1 1 1 a*X+a^2 a^2*X+a^2 X+1 X+1 X a^2 X+a^2 a^2 a*X X+a a^2 1 1 a*X+a 1 X+a^2 1 a*X a^2*X+a a*X a^2*X 1 a^2*X+1 a*X+a X a*X+a 0 a*X+a^2 a^2*X a^2*X+1 a^2 a a*X a*X+1 a*X+a^2 a^2*X a^2*X+a a^2*X+a^2 1 a*X a^2*X+1 X 0 0 1 0 0 X X a^2*X+1 a a^2*X+a^2 a*X 0 a*X a*X X+1 a^2 a*X+a^2 a a*X+a a^2*X+a^2 a*X+a a^2*X+1 1 a^2*X+a a^2*X+a^2 X+a a^2*X a*X+a a*X+1 X+1 a*X+a^2 X a*X+1 a^2*X+a a*X a a^2*X+1 a*X+a^2 a^2*X+a a^2 X a^2*X+a a^2 a^2 X a^2*X a^2*X+a 1 0 X+1 X+a^2 X+1 X+a a*X+1 a^2 a*X+a^2 a*X a*X+a^2 a^2*X+1 X+1 a*X+a^2 a^2*X+1 a*X a*X a*X+1 1 1 a^2*X+1 X+a^2 a*X+a^2 X a*X+1 a^2*X a a*X+a 0 1 X a*X+a^2 X+a a*X+a 0 0 0 1 1 a^2*X+a a^2*X+a^2 a^2 X+a^2 a*X+a^2 a^2*X+a^2 X+1 a X a^2*X a a^2*X+1 a^2*X+a^2 0 X+a a^2 X+a^2 a*X+a^2 a^2*X+1 a^2*X+a 0 a^2*X+a^2 X+a^2 X+a a*X a*X a*X+a X+1 1 a X a*X+a a^2*X+1 a*X+1 1 a^2 0 a^2*X+1 a*X a*X+1 a*X+a a^2*X+a^2 a^2*X+a a*X+a^2 X+a a*X+a a*X X+1 a^2*X+1 a^2*X a^2*X 1 X+a^2 X+a a^2*X+1 1 1 a*X+1 a*X+a a^2*X a^2*X+1 a*X+1 0 a^2 a*X+a a a^2*X+a^2 a^2 X+a X+1 a^2*X X+a^2 a^2*X+1 a a^2*X+a^2 a^2*X+1 generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 227. Homogenous weight enumerator: w(x)=1x^0+648x^227+546x^228+1020x^229+2724x^231+1476x^232+2256x^233+4668x^235+2544x^236+2604x^237+4836x^239+3060x^240+3432x^241+5016x^243+2742x^244+3168x^245+5208x^247+2892x^248+2928x^249+4248x^251+1938x^252+1836x^253+2388x^255+843x^256+1080x^257+864x^259+288x^260+108x^261+108x^263+48x^264+12x^267+6x^268 The gray image is a linear code over GF(4) with n=324, k=8 and d=227. This code was found by Heurico 1.16 in 337 seconds.