The generator matrix 1 0 1 1 1 X+2 1 1 2 X 1 1 1 1 0 1 X+2 1 1 1 X 1 1 2 1 X X+2 1 1 1 1 1 1 0 1 X 1 1 1 2 1 0 1 X 1 X+2 1 1 1 1 1 0 1 0 1 X 1 X+2 X 2 1 0 1 2 X 2 0 1 1 1 X+2 0 2 1 1 1 1 0 1 1 0 X+3 1 X X+1 1 1 X+3 2 X+2 1 1 X 1 0 X+1 1 1 X 3 1 X+1 1 1 X 3 0 X+2 3 X+1 1 2 1 X+3 1 X+3 1 X 1 X 1 X+3 1 X+2 X+2 X+1 X+3 3 1 0 1 X 1 3 1 1 1 2 1 X+1 X 1 X X 2 X+2 0 1 X 1 1 0 X 2 0 0 X 0 X+2 0 0 0 2 2 2 X X+2 X+2 X X+2 X X+2 X+2 2 X+2 2 2 X X+2 X+2 0 2 0 2 X+2 X 2 X+2 2 X 2 0 0 0 0 X X X+2 X+2 2 0 0 2 X X 0 X+2 2 0 X X+2 0 X+2 2 0 0 0 X X+2 X+2 2 X+2 X+2 2 0 X+2 X X+2 2 0 0 0 0 0 X 0 0 X 2 X+2 X X 0 X+2 X X 2 X X X+2 2 0 0 X 0 2 X+2 X X 0 2 X X+2 2 X X 2 X+2 X+2 X X 0 2 2 0 X X 2 2 2 0 X+2 X X+2 0 0 X X 0 X+2 0 0 0 X+2 2 X+2 2 X+2 X X X+2 X+2 X+2 0 X+2 X X+2 X 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 0 2 2 0 0 2 2 2 2 2 0 0 2 0 2 0 0 2 0 0 0 2 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 0 0 2 0 2 2 0 2 0 0 2 2 2 0 2 2 0 0 0 2 2 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 0 2 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 2 0 0 0 2 0 0 2 0 2 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 0 2 0 2 2 0 0 0 0 2 2 0 2 0 0 2 0 2 0 2 2 2 2 2 2 0 0 0 0 0 2 0 2 2 2 2 0 2 2 0 0 2 0 2 0 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+83x^68+166x^69+212x^70+490x^71+321x^72+680x^73+485x^74+818x^75+452x^76+914x^77+506x^78+824x^79+472x^80+640x^81+239x^82+354x^83+155x^84+130x^85+69x^86+48x^87+37x^88+24x^89+19x^90+20x^91+14x^92+6x^93+4x^94+6x^95+1x^96+1x^98+1x^102 The gray image is a code over GF(2) with n=308, k=13 and d=136. This code was found by Heurico 1.16 in 5.75 seconds.