The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 0 1 1 X+2 1 X 1 0 1 1 1 0 1 1 1 X+2 1 1 X+2 1 2 1 X+2 1 0 1 0 1 1 1 1 2 1 1 1 1 X+2 1 1 1 X+2 1 1 1 X X+2 X+2 1 1 1 1 X 1 1 0 1 1 0 1 1 1 1 1 X 1 0 X+2 1 1 1 2 0 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 X+2 1 X+1 0 X+1 1 X+2 0 3 1 0 3 1 X+1 1 2 1 X+3 1 X+1 1 X+2 X 2 3 1 3 X+1 2 X+2 1 1 2 2 1 X 3 X+2 1 1 1 X+1 1 X+3 X+2 0 1 X+3 X 3 2 1 X X+1 X+1 X+3 0 X 0 1 1 X+3 1 X+1 2 X 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 2 2 0 2 2 2 2 2 2 0 2 2 0 0 0 2 0 2 0 2 2 0 0 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 2 2 2 0 2 2 2 2 2 2 0 2 2 2 0 2 0 0 0 0 0 2 2 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 2 2 2 2 0 2 0 0 2 0 2 2 2 0 2 2 2 2 0 2 2 0 0 2 2 0 0 0 2 0 0 0 0 2 0 0 2 2 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 0 2 0 0 2 0 0 2 2 2 0 2 2 2 2 0 0 2 2 2 2 2 2 0 2 0 2 0 0 2 0 2 2 0 2 0 0 2 2 0 0 0 2 2 0 0 0 0 0 0 2 0 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 2 2 0 0 2 0 0 0 0 0 0 2 0 0 2 0 2 0 0 2 0 2 2 2 0 0 2 2 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 0 2 2 2 2 2 2 2 2 2 2 2 0 0 2 0 0 0 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 2 0 0 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 0 2 2 2 2 2 0 0 2 0 2 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 0 2 2 2 2 2 2 0 0 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 0 2 2 2 0 0 2 0 2 2 0 0 0 0 0 0 0 0 2 2 0 2 2 0 0 0 0 2 0 0 2 0 0 2 2 0 2 2 2 2 2 0 2 2 0 2 0 0 2 2 0 0 2 2 2 2 0 0 2 2 0 2 2 2 2 0 0 2 0 0 0 0 2 2 2 2 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 2 generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+40x^77+126x^78+88x^79+305x^80+132x^81+405x^82+128x^83+452x^84+106x^85+524x^86+162x^87+500x^88+146x^89+380x^90+98x^91+230x^92+70x^93+80x^94+30x^95+32x^96+18x^97+14x^98+6x^99+12x^100+3x^102+2x^104+2x^108+1x^110+1x^114+1x^118+1x^126 The gray image is a code over GF(2) with n=344, k=12 and d=154. This code was found by Heurico 1.16 in 68.7 seconds.