The generator matrix 1 0 0 0 1 1 1 2 1 1 X^2+2 X^2+X 1 0 1 X X^2+X+2 1 1 X^2+X 1 1 X+2 X^2+X+2 1 1 1 0 1 X^2+X+2 X^2 X+2 X^2+2 1 1 X^2+2 X^2 1 X^2+X+2 1 X^2 1 X^2+X+2 1 0 X 1 1 1 1 X 1 1 X^2+X+2 1 1 X^2 X^2+X+2 1 1 0 X^2+X 0 1 1 X^2+2 X^2 1 1 1 1 X 1 0 1 0 0 0 3 3 1 1 X^2+X+2 2 1 X^2+X 1 X^2+1 2 1 X^2+2 X^2+2 1 X^2+X+2 X+3 1 1 X+1 0 X^2+1 1 X+1 X^2 X^2+X 1 X+2 X^2+X+1 X^2+X+3 1 1 1 0 3 X X+2 X^2+2 X^2+X+3 1 1 X^2+3 X^2 0 X^2+X+1 1 2 X+2 X+2 X^2 X+3 1 1 3 X^2+X+2 1 1 1 X^2+X+3 2 X 1 X^2+X+3 X X+3 3 X+2 2 0 0 1 0 1 1 X^2 1 3 X^2 1 0 X+3 X+1 2 X^2+X 3 3 X^2+X+1 X+1 X 0 X^2 X^2+X 0 X+2 X^2+3 X^2+3 X+3 1 1 X^2+X+2 1 X^2+3 X X+1 X+2 X^2+X+2 1 X+1 1 1 0 X+2 X^2+X X X^2 X^2+3 X^2+2 X+2 X^2+2 X+1 X+2 1 X^2+X X^2+X+1 X+1 X^2 3 X^2+X+3 X^2+2 X+1 X^2+3 X^2+2 X^2+X+1 X X^2+1 2 X^2+X+2 2 X^2+X+3 X+2 0 0 0 0 1 1 X^2 X^2+1 3 X+1 X^2+X+1 X^2+X+3 X^2+X+1 2 X^2+X+2 X 1 X X^2+X+2 X+1 X^2+1 3 X+3 X^2+X+2 X^2+1 0 X^2+X+2 3 X^2+X+2 X+2 X^2+X+2 3 X^2+X X+1 X^2+X 3 X^2+X+1 1 X^2+X 2 X^2+3 X^2+X X^2+X+2 1 X+2 2 X^2+X+3 1 3 0 X^2+X+3 X^2+X+2 X^2+X X+3 1 X X^2+X+3 X^2 X+3 X+2 X^2+1 X^2+X 1 1 X^2+X+2 3 1 X^2+X+1 3 3 X^2+X+3 0 1 0 0 0 0 0 X^2+2 0 X^2+2 X^2+2 X^2 X^2 X^2 X^2 0 2 2 X^2+2 2 2 X^2 X^2+2 X^2+2 X^2 0 X^2 2 0 X^2 0 0 0 X^2 0 2 X^2+2 0 0 0 X^2 X^2 2 X^2+2 X^2 2 X^2+2 X^2 0 2 0 X^2 2 X^2+2 X^2+2 0 X^2+2 X^2 2 2 2 X^2+2 X^2 X^2 X^2 2 X^2 X^2 2 X^2+2 X^2+2 0 0 X^2 0 X^2 generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+133x^64+932x^65+2718x^66+4924x^67+9891x^68+14006x^69+21713x^70+26102x^71+33749x^72+33128x^73+34117x^74+26992x^75+22313x^76+13798x^77+9192x^78+4474x^79+2265x^80+882x^81+530x^82+156x^83+60x^84+36x^85+9x^86+6x^87+4x^88+2x^89+7x^90+2x^94+2x^95 The gray image is a code over GF(2) with n=584, k=18 and d=256. This code was found by Heurico 1.16 in 665 seconds.