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 X 1 1 1 1 1 1 X 1 1 a*X 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 1 a*X+1 a*X+a a^2 0 a^2*X+1 a*X 0 a*X X+a 1 1 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^2 X+1 X a*X+a a*X a*X+a^2 a^2*X+1 1 a^2*X+a a^2*X a^2*X+a a*X+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*X X 0 0 0 X 0 X a^2*X a*X X 0 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+768x^258+744x^259+159x^260+1632x^262+1248x^263+273x^264+1848x^266+1092x^267+147x^268+1536x^270+972x^271+132x^272+1248x^274+876x^275+99x^276+1080x^278+564x^279+87x^280+588x^282+360x^283+81x^284+372x^286+240x^287+21x^288+108x^290+48x^291+18x^292+36x^294+6x^296 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 46.5 seconds.