The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X 2 0 0 1 1 1 1 X+2 1 1 1 1 X X X 1 1 2 1 0 1 1 1 1 1 1 2 2 X X+2 1 X 1 0 1 1 1 X 0 X 1 1 0 1 2 1 1 1 1 1 1 1 1 0 1 1 X 1 1 1 X+2 1 1 1 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 X+2 1 1 1 2 3 X+3 X 1 0 X X+3 1 X 1 1 0 X+1 1 2 X+2 X X+2 X+1 1 X+1 2 1 1 1 0 1 1 X+1 0 2 1 3 1 X+2 1 X+3 1 X+2 X+2 1 X+3 X+2 X X+2 X+2 X+1 X+2 3 X+2 0 X+2 1 1 0 X 1 2 X+3 X+2 0 0 1 1 X+3 X+2 1 X+1 X+2 1 1 0 1 X X+1 1 1 0 X+1 2 0 X+3 X+2 1 X 1 X+3 X+2 X+2 X 1 X+2 1 X+1 0 X+3 1 0 X+1 X+3 X 1 1 0 2 X 1 1 3 X+3 2 1 X+2 1 X+2 1 X+1 X X+3 1 X+3 X+3 X+2 2 X X 1 0 2 3 X+2 X+3 X 1 0 X+3 X+3 0 0 0 2 0 0 0 0 2 2 0 0 0 2 0 2 0 0 2 0 2 0 0 0 2 2 2 0 2 0 2 2 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 0 2 2 0 0 2 0 0 2 2 0 0 2 2 2 0 0 2 0 0 0 0 0 2 0 0 2 2 2 0 2 2 0 2 2 0 2 2 0 0 2 2 2 2 0 2 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 2 2 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 2 2 0 2 2 2 2 0 0 2 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 0 0 0 2 0 0 2 2 2 0 2 2 0 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 2 0 0 0 2 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 0 2 0 2 2 2 2 2 0 0 0 0 2 0 2 2 0 0 0 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+130x^69+186x^70+454x^71+406x^72+790x^73+509x^74+916x^75+542x^76+872x^77+513x^78+712x^79+339x^80+538x^81+283x^82+404x^83+154x^84+206x^85+88x^86+66x^87+22x^88+14x^89+15x^90+8x^91+8x^92+8x^93+5x^94+2x^97+1x^98 The gray image is a code over GF(2) with n=308, k=13 and d=138. This code was found by Heurico 1.16 in 4.5 seconds.