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 X 1 1 X^2+2 X+2 1 1 1 1 1 X^2+2 X^2+X+2 0 1 X^2 1 1 X^2 X+2 X^2+2 X^2+2 1 1 X^2 X^2+2 1 X^2 X^2+X X^2+2 1 1 1 1 1 1 0 X 1 1 1 X^2+2 X 1 1 X+2 1 1 X^2+2 1 1 X+2 1 1 X^2+X 1 2 2 1 X^2 1 1 1 0 1 0 0 X X^2+1 3 X^2 1 X+3 X^2+X X+1 1 1 X+2 X^2+2 X^2+X+2 1 X^2+2 1 X^2+X+3 2 2 X^2+3 X^2+X+1 1 1 1 X X^2+X+2 X+2 X^2+1 1 1 X+2 X^2+2 0 X^2+1 X^2+2 1 X^2+2 X 1 X+2 X+3 0 X^2 X^2+1 X+1 X^2+2 1 1 3 0 X^2+3 1 X+2 X+2 2 1 X^2+X+3 3 X^2+X 0 1 X^2+2 3 X^2+X+3 1 X^2+X+3 2 1 X^2+X+1 X^2+X X^2+2 X^2+X+2 0 0 0 1 0 0 X^2 1 X^2+1 1 X^2+1 3 2 0 3 1 1 X+2 X^2 1 X^2+X+3 X+1 3 3 X+3 X^2+2 X+2 X^2+X+2 X^2+X+1 2 X X^2+X+3 X^2+X+3 X^2+3 X^2+2 1 1 X+3 X+3 X+2 X+1 X X^2+2 X 1 X^2+2 2 1 X+2 X^2+X 0 1 X^2+3 2 0 X^2+X+1 1 1 X^2+X+3 X^2+1 X 0 X^2+X+1 X^2 X+3 X^2+X X^2+X+2 2 X X+1 1 1 X^2+X+2 X+3 1 X^2+X+1 X^2+X+1 0 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 2 X^2+3 0 X+1 X^2+X X^2+1 X^2 X 3 2 X^2+X+3 X^2+X+1 X^2+X+2 X+1 X+3 X^2+X+2 1 X^2 X+2 1 X+2 0 X+3 X+1 3 1 X^2+X X^2+1 1 X^2+1 3 X^2+X+1 X^2+X+2 X+2 X^2+2 0 3 X 1 X^2+1 X^2+2 X^2+2 X+3 X+2 X+3 2 1 X^2+X+1 X^2+1 1 X+1 X^2+X 1 X+3 X^2+3 1 X^2+X+1 X^2+1 X^2+X+1 X X^2+X+1 3 X+1 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2+2 2 X^2 X^2 X^2 X^2+2 0 2 X^2+2 X^2+2 2 X^2+2 X^2+2 2 X^2+2 2 2 2 0 2 X^2 X^2+2 X^2 0 X^2+2 2 0 X^2+2 2 0 X^2+2 0 X^2+2 X^2+2 2 X^2+2 X^2 X^2+2 X^2+2 2 X^2 X^2 0 X^2+2 2 X^2 0 X^2 0 0 X^2+2 2 X^2 0 X^2 X^2 X^2+2 2 X^2 X^2+2 X^2 X^2+2 0 generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+315x^68+1230x^69+3150x^70+6170x^71+9616x^72+15266x^73+20291x^74+26850x^75+31266x^76+32368x^77+32154x^78+27786x^79+21747x^80+14840x^81+8925x^82+5426x^83+2476x^84+1274x^85+527x^86+300x^87+78x^88+56x^89+6x^90+12x^91+3x^92+4x^93+2x^94+2x^97+2x^100+1x^102 The gray image is a code over GF(2) with n=616, k=18 and d=272. This code was found by Heurico 1.16 in 646 seconds.