The generator matrix 1 0 0 0 1 1 1 1 X^2+2 X+2 1 1 X^2+X+2 X^2+X+2 1 X^2 1 1 1 X+2 X^2+2 1 X^2+X+2 1 X^2+2 1 1 1 X^2+X+2 X+2 1 1 1 1 2 X X^2 0 1 1 0 X^2 0 1 1 1 1 X^2 1 1 1 X^2+2 1 X+2 1 1 X 2 1 X+2 1 1 X 1 1 1 1 1 X+2 1 X^2+2 1 1 1 1 1 1 1 0 1 0 0 X X^2+1 X^2 3 1 1 X^2+X+2 3 1 X^2+X 3 1 X^2+3 1 X+3 1 1 X^2+X 0 3 1 X+2 X^2+2 X^2+2 2 2 X^2 X^2+X+1 0 X+1 X X^2+X 1 1 X^2+X X^2+X+3 1 X 1 0 X^2+X+2 X^2+X 2 1 0 X+3 2 1 X^2+1 1 X^2+3 X^2+2 1 1 X^2 X X^2+X+1 X X+2 X^2+2 X^2+X+2 X^2+3 X+1 1 X 2 1 X^2+X+1 1 X^2+X 3 2 X^2+2 X+2 0 0 1 0 0 X^2 1 3 X^2+1 2 X^2+X+1 X+1 X^2+X+1 1 X^2+X+2 X+3 X^2+X 3 1 X^2+X+3 2 X^2 X^2 X+2 X X^2+3 X+1 X^2+2 1 1 X X^2+X 1 X+3 X^2+X+2 1 3 0 X+2 0 X^2+X+2 1 X^2+X+3 X^2+X+3 X+1 X^2+X+2 X^2+1 2 0 X+2 X X^2+X+3 X^2+X+1 X X^2 1 X^2+2 3 2 1 X^2 X+3 1 X^2+1 X 2 X+1 3 2 X^2+X+1 X^2+2 3 X^2+X 0 X X+3 X^2+1 0 0 0 0 1 1 X^2+X+1 X+1 X^2+2 X+1 3 X^2 X^2+3 2 X^2+1 0 X^2+X+1 X^2+X+1 X^2+X X^2+X+1 X+2 X^2+X+3 X^2+2 1 X^2+X X^2+X+2 X^2+X+2 X+3 X^2+X+1 X^2 X^2+3 X^2+2 X^2+X+3 2 X^2 1 X^2+X+1 X^2+1 X^2+1 X^2+3 X^2 X^2+2 X^2+X X+2 1 X^2+X+2 X^2 X+2 X+2 X^2+X+3 X^2+X X+2 3 X+3 X+3 X^2+X+1 X^2+3 X+2 X^2+X+1 X^2+X X^2+X+3 X+3 X^2+X+3 X^2+2 X+3 0 X^2+1 0 1 1 X^2+3 X X^2+2 3 3 X^2 2 X^2 X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2+2 X^2+2 2 2 2 X^2 X^2+2 X^2 2 0 X^2+2 2 X^2 0 2 2 X^2+2 X^2 X^2+2 2 X^2 X^2 0 X^2 2 2 2 0 X^2+2 0 X^2+2 0 2 0 0 X^2 0 X^2+2 0 0 2 X^2+2 X^2+2 X^2 X^2 0 X^2 X^2 2 0 X^2 X^2 0 0 X^2+2 2 2 X^2+2 0 2 X^2+2 X^2 X^2+2 X^2 X^2+2 generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+216x^69+1426x^70+2900x^71+5928x^72+9248x^73+15065x^74+20666x^75+27341x^76+31808x^77+32855x^78+31988x^79+27981x^80+20620x^81+14843x^82+8854x^83+5708x^84+2644x^85+1181x^86+460x^87+221x^88+108x^89+37x^90+12x^91+17x^92+12x^93+3x^96+1x^98 The gray image is a code over GF(2) with n=624, k=18 and d=276. This code was found by Heurico 1.16 in 654 seconds.