The generator matrix 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 a a^7*X+a^2 a^3 a^7*X+2 a^7*X+a^6 a^5 a^7 0 a^7 a^5 a a^7*X+a^6 a^7*X+1 a^7*X+a^2 a^3 a^7*X+2 1 0 a^7*X+a^6 a^7 a^5 a^3 a a^7*X+2 a^7*X+a^2 a^7*X+1 X a^6*X+a^2 X+a a^6*X+a^6 a^7*X+1 a^6*X+2 a^6*X+2 X X+a^5 a^2*X+a 2*X+1 a*X+a^5 X+a a^2*X+1 a*X+a^5 a^6*X a^6*X+a^2 a^5*X+a^6 X+a^3 a*X+a^6 X a^3*X+a a^3*X+2 a*X+a a^6*X+a^2 a^6*X+2 a*X a X+a^2 2*X+a^2 a^5*X+a^6 2*X+a^6 X a^5*X+a^6 a^5*X+a^2 a^6*X+a a^2*X+a^5 a^5*X+a^2 a^5*X+a^6 a*X+a^5 X+a^3 a*X+a^5 1 0 0 0 0 a^7*X 0 a^7*X X a^6*X a^6*X 2*X a*X a^7*X a*X X 0 a^5*X a^3*X a^6*X 2*X a^3*X 0 a^5*X a^3*X a^5*X a^3*X 2*X a*X a^2*X a^5*X a^2*X X a^3*X a*X a^3*X 0 a^7*X a^7*X X a^2*X a^6*X a*X 2*X a^7*X a^2*X a^6*X a*X X a^5*X 0 2*X a*X X a^5*X a*X a^2*X X X a^2*X a^3*X 0 a^2*X 2*X a^5*X a*X a^2*X X a*X a^5*X a^5*X 2*X a^3*X a^6*X 2*X 0 a^2*X 0 0 0 X a^7*X a^7*X X a*X X a^2*X a^5*X a^6*X a^5*X a*X a^2*X a^7*X 0 a^3*X a*X a^3*X a^6*X a^6*X 2*X a^3*X a*X X X a^5*X a^7*X 0 0 a^7*X a*X a^6*X a*X 0 2*X 0 a^6*X a^6*X a^2*X a*X 2*X 2*X X a^2*X a^6*X a^6*X 0 a^6*X X X a^5*X a*X a^5*X a^7*X 2*X 2*X a^7*X 0 2*X 2*X a^2*X a^7*X 0 a^7*X 2*X X a*X a^6*X a*X a^5*X 2*X a^2*X generates a code of length 74 over F9[X]/(X^2) who´s minimum homogenous weight is 558. Homogenous weight enumerator: w(x)=1x^0+400x^558+72x^563+504x^565+2448x^566+2256x^567+144x^568+720x^570+1296x^571+2088x^572+3600x^574+14616x^575+6816x^576+3456x^577+4320x^579+5832x^580+6912x^581+9504x^583+28944x^584+11904x^585+27648x^586+18360x^588+19440x^589+20448x^590+20664x^592+63432x^593+20920x^594+73728x^595+29088x^597+25920x^598+22968x^599+18216x^601+48024x^602+15080x^603+520x^612+400x^621+328x^630+328x^639+96x^648 The gray image is a linear code over GF(9) with n=666, k=6 and d=558. This code was found by Heurico 1.16 in 44.8 seconds.