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+X+2 1 0 1 X+2 X^2 1 X^2+2 2 1 X^2 1 1 1 X+2 1 1 1 1 X^2+X 1 X^2 X^2+X+2 X^2+2 1 1 X^2+2 X X 1 2 0 1 1 1 X^2+X 1 1 X+2 1 1 X^2+2 1 2 2 1 1 1 X^2 0 X+2 X^2+X+2 2 X 1 1 1 1 X+2 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+X+3 X^2 3 1 X+1 1 1 X^2+1 1 X^2+X+2 0 2 2 X^2 2 1 X X^2 X+2 X+1 2 X+2 X^2+X 1 1 X+1 3 1 2 1 X^2+X+2 X^2 X^2+2 X^2+1 X+2 X^2+3 1 X^2+1 X+2 1 2 0 2 X^2+X+1 X^2+X+2 0 X+3 X^2+2 X^2+1 X 1 X+2 X+2 1 1 X^2+2 X X^2 X+1 X^2+X X^2+2 0 0 1 0 0 X^2 1 X^2+1 1 X^2+1 3 2 0 3 1 2 1 3 X^2+1 3 3 X^2+X+2 X^2+X X 1 X^2+2 X+2 X^2+2 X^2+3 X^2+1 0 3 X+2 X^2 X 1 X^2+1 X^2+X+2 2 X^2+X+3 X^2+X+1 X^2+X+1 X+3 1 X+1 X^2+X 1 X 3 X^2+1 X^2+1 X^2+X X^2+X+3 X+3 X^2+1 X^2+1 X^2+X 1 X+2 X^2+X 1 2 X^2+X X^2+X+3 X 1 X^2+2 1 X^2+X+2 X^2+3 0 X^2+X X^2+1 X+2 X^2+X 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 2 X^2+3 X+1 X 3 2 X+2 X+1 X+1 X^2+X+2 X X^2+3 X+1 1 X+2 1 0 X^2+1 3 X^2+X+3 X+2 X^2 X^2+2 X^2+2 1 0 X+1 X+1 X^2 0 X^2+3 1 X X^2+X+3 1 X X+1 X^2+3 X+3 X^2+3 X^2+3 X^2+2 2 X^2+3 1 1 1 X^2+X+1 X^2+X+3 X^2+X+2 2 1 X+2 1 X+2 X^2+X+2 2 X^2+2 X+2 X^2+X+3 X^2+X+3 1 X^2+2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2+2 X^2+2 X^2 2 2 X^2+2 X^2+2 2 0 X^2 0 2 X^2 X^2 X^2+2 2 2 0 X^2 2 X^2 0 2 X^2 0 0 X^2+2 X^2+2 0 2 2 0 X^2+2 2 0 X^2+2 X^2+2 X^2+2 X^2+2 2 X^2+2 X^2+2 2 X^2+2 X^2+2 2 X^2 0 2 0 X^2+2 2 2 2 X^2 0 X^2 X^2 X^2+2 0 2 0 generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67. Homogenous weight enumerator: w(x)=1x^0+160x^67+1112x^68+3096x^69+5727x^70+8928x^71+15109x^72+20254x^73+27759x^74+31292x^75+34954x^76+31808x^77+27720x^78+21018x^79+15184x^80+8296x^81+5120x^82+2600x^83+1193x^84+432x^85+189x^86+84x^87+62x^88+18x^89+9x^90+12x^91+1x^92+4x^94+2x^95 The gray image is a code over GF(2) with n=608, k=18 and d=268. This code was found by Heurico 1.16 in 691 seconds.