The generator matrix 1 0 0 0 1 1 1 1 X^2+2 1 1 1 X^2+X+2 X X+2 X 1 X^2+2 X^2 X 1 1 1 1 X^2+X+2 X+2 1 1 1 1 2 X^2+X 1 X^2 X 1 X^2+2 1 X^2+2 X^2+X 1 1 X^2 1 1 X^2+X 2 1 1 1 1 X^2+2 2 2 1 1 1 X^2+X+2 1 X^2+X+2 X^2+2 1 1 X^2+2 2 X^2+X 1 X^2+2 X^2+X 1 1 1 X+2 X 1 0 1 0 0 X X^2+1 3 X^2 1 X+3 X^2+X X+1 1 1 2 X^2+X+2 X+2 0 1 X X+3 X^2+2 3 X^2+X+2 1 1 0 X^2+1 X^2+1 X+3 0 1 X^2+X+2 1 1 X+2 1 1 X^2+X+2 1 X^2+3 X^2+X+3 X X+2 2 X+2 1 0 X+3 1 X+2 1 X+2 1 X+1 X^2+2 X+2 1 X^2+X 1 1 X^2 X+1 0 X^2+X+2 X^2 X^2+2 1 X^2+2 X^2+X X^2+X+2 X^2+X+1 0 2 X^2+2 0 0 1 0 0 X^2 1 X^2+1 1 X^2+1 3 2 0 X^2+X+1 1 1 X^2+X+2 X^2+X X^2+2 1 X^2+X+2 X+1 X^2+X+3 X+1 1 X^2+3 2 X+2 X^2+X+1 X^2+2 1 X^2+X X^2+2 X+1 X^2+X+2 0 X^2+X+2 3 1 3 X^2+3 X^2+3 X^2+X+2 X^2+X+3 X^2+X+3 1 X^2 0 X^2+2 X^2+3 X^2+X+2 X^2+2 X X^2+3 X^2+X X+2 X+3 2 X^2+X+2 X^2+X+3 X^2+X+1 X+2 0 1 X^2+2 2 X^2+3 X+1 1 X^2+X+1 X^2+1 X^2 1 0 X^2+2 0 0 0 1 1 X^2+X+1 X^2 X^2+X+3 X^2+X+1 X^2+1 X^2+X+2 X^2+X X+1 X^2 X+3 X X 1 X^2+X X^2+1 X^2+X+1 X+1 X+2 0 1 X^2 X^2+X+3 X+2 X^2+X+3 X^2+X+1 X^2+X+1 X+1 X^2+2 X^2+X 1 X^2+X 2 X^2+3 X+3 X^2+3 X^2+X+3 X 1 X^2+X+2 X+3 X X^2+2 X^2+X+2 2 X X^2+3 X^2+X+3 1 X^2+3 X^2+X+2 X+1 3 X^2+X+1 0 X^2+3 X+2 X^2+1 X^2+1 1 1 1 3 X X^2+3 X^2+1 X+2 X^2 0 1 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 2 2 2 X^2+2 0 2 X^2 X^2 2 X^2+2 X^2+2 X^2+2 0 X^2 2 X^2+2 X^2+2 2 2 X^2+2 X^2+2 2 X^2+2 2 X^2+2 X^2 X^2 X^2+2 2 X^2 X^2 X^2 X^2 X^2+2 X^2+2 0 0 2 X^2+2 2 0 2 0 2 2 2 0 2 X^2+2 X^2+2 2 X^2 X^2 X^2 0 generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+168x^66+926x^67+2978x^68+5592x^69+9465x^70+14386x^71+21295x^72+26182x^73+33453x^74+32824x^75+33892x^76+26450x^77+21967x^78+14436x^79+8892x^80+4906x^81+2500x^82+1050x^83+438x^84+168x^85+94x^86+42x^87+16x^88+12x^89+1x^90+6x^92+2x^93+2x^96 The gray image is a code over GF(2) with n=600, k=18 and d=264. This code was found by Heurico 1.16 in 668 seconds.