The generator matrix 1 0 0 1 1 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 0 1 a*X 1 1 1 1 1 X 1 a*X 1 1 a^2*X 1 a*X X 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 X 0 1 1 1 1 1 X 1 1 1 1 1 1 0 1 1 1 a*X 0 1 1 1 1 1 1 1 1 X 1 1 a^2*X 1 1 1 1 1 0 1 0 0 X a^2*X 1 a^2*X+a a^2 1 a 1 a^2*X+1 a^2*X+1 X+a^2 a^2*X+a X+a^2 a 1 a^2*X+a^2 1 a^2*X+a^2 X a^2*X a*X+1 a^2*X+a^2 X X+1 1 0 a*X+a 1 a^2*X+a 1 1 X+a^2 a*X+a a^2*X+a^2 X+a^2 a*X+1 a^2 a a^2*X X+1 X+1 1 1 a^2*X+a a*X a^2*X+a^2 a 1 0 1 a*X X a X+a^2 a*X+1 a^2*X+a^2 1 a^2*X+1 X a^2*X+1 a*X+1 a*X+a^2 X+1 X 0 a*X+a^2 a*X+1 0 1 a*X a*X X+a a^2*X+a^2 a^2 X a*X+1 X+a^2 0 X+a X+1 1 a^2 1 a*X a*X a 0 0 1 1 a^2*X+a a^2 X+1 a^2*X+1 a*X+1 a^2 0 a*X+1 a X a^2*X a^2*X+a^2 X+a^2 a*X+a a a^2*X+a a*X+a^2 a*X+a a^2*X X+a^2 a a^2*X 1 0 a*X+1 a a*X+a a^2*X X a X+a^2 a*X+a^2 X+a^2 1 a^2 a^2*X+1 a^2*X+a a^2 X+a a*X+1 a^2*X+a^2 a*X+a a^2*X X+1 a^2*X+1 a^2*X a^2*X a^2*X+a^2 0 X+a^2 1 X+a^2 a^2*X+a X+a X+1 0 a^2*X+1 a*X+a X+a a*X a^2*X+a^2 a^2 a*X+a^2 1 a*X+a^2 1 X 1 0 a 1 a*X+a^2 a^2*X+1 a*X+1 a*X X+a a^2*X+a 1 X+1 X+a^2 a*X a*X+a X+a^2 a^2*X+a a^2 1 0 0 0 a^2*X 0 0 a^2*X a^2*X a^2*X X a*X X 0 a*X a*X X X a^2*X X a^2*X a*X X a^2*X a^2*X a^2*X 0 a^2*X a^2*X a^2*X a*X a*X a^2*X 0 0 X a^2*X 0 a*X 0 a*X a*X a^2*X X X a^2*X a^2*X a*X a*X X a^2*X X 0 a*X a^2*X X a*X 0 a*X 0 X 0 X X a*X a^2*X a*X a*X a*X X 0 0 0 a*X 0 a*X a^2*X 0 X a^2*X a*X a^2*X a^2*X 0 0 X 0 a*X a*X a^2*X a^2*X generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 258. Homogenous weight enumerator: w(x)=1x^0+780x^258+624x^259+126x^260+1824x^262+1272x^263+279x^264+1536x^266+1368x^267+153x^268+1632x^270+888x^271+147x^272+1248x^274+816x^275+120x^276+984x^278+540x^279+117x^280+648x^282+336x^283+45x^284+456x^286+168x^287+24x^288+108x^290+120x^291+12x^292+12x^295 The gray image is a linear code over GF(4) with n=360, k=7 and d=258. This code was found by Heurico 1.16 in 20.7 seconds.