The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 0 1 0 1 1 1 X 1 1 X 1 1 X X 1 1 1 1 1 0 0 1 1 1 X 1 X 1 1 X+2 1 0 1 1 1 0 X 1 1 1 X+2 1 1 X 0 1 0 X+2 1 X+2 1 0 2 1 1 X 1 1 0 X 1 X+2 1 1 1 1 0 1 1 0 X+3 1 X X+1 1 3 1 X+2 X+3 0 1 X+3 1 2 X+2 1 1 X+2 3 1 X+3 X 1 1 2 X+1 3 2 X 1 1 1 X+2 0 1 X+1 1 0 X+3 1 X+3 1 3 0 X 1 1 X+1 0 X+2 1 X+1 3 1 1 1 1 1 3 1 X+3 1 X 1 0 2 3 1 1 1 X+2 1 X+3 1 X+1 X+1 0 0 X 0 X+2 0 0 X 0 X+2 0 0 0 X X+2 2 X+2 X+2 X 2 X X 0 X X X+2 X 2 X X 0 2 X+2 2 X+2 0 2 0 X+2 2 X+2 2 2 X 0 X X 2 X+2 0 X 2 2 X+2 2 0 2 X+2 X X+2 2 X X+2 2 0 X+2 0 X+2 0 X X 0 X+2 0 0 0 X 2 X+2 2 0 0 0 X 0 0 X X X X X+2 2 X X X+2 0 2 2 X+2 X 2 X+2 0 X+2 2 0 0 2 2 X 2 X+2 2 2 0 X+2 X+2 2 0 X X+2 2 X 2 0 0 2 2 X X+2 X+2 2 X+2 0 0 X+2 X X 2 0 X+2 2 X+2 0 0 2 X+2 0 X 0 2 0 0 X X+2 X X X+2 X 0 0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 0 2 0 2 0 2 0 0 2 0 2 0 2 0 0 0 0 2 0 0 2 0 2 2 2 0 0 0 2 2 0 2 2 2 2 2 0 2 0 0 2 2 0 0 2 2 0 2 2 2 2 2 2 2 0 2 0 2 0 2 0 2 2 2 2 0 0 0 0 0 2 0 0 2 2 2 0 0 0 2 2 2 0 0 0 2 0 0 0 0 0 2 2 2 2 0 2 2 0 0 2 0 0 0 0 2 2 0 2 2 0 2 2 0 0 0 2 2 2 2 0 0 0 2 2 2 2 2 0 0 2 0 2 2 0 0 2 0 2 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 2 2 2 0 0 0 2 2 2 0 0 2 2 2 2 0 0 2 2 2 0 0 2 2 2 2 0 0 0 2 0 0 2 2 0 0 0 2 0 2 0 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 0 0 0 0 2 0 2 0 2 2 0 2 0 2 0 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 0 2 0 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 0 2 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+46x^69+130x^70+232x^71+314x^72+426x^73+668x^74+764x^75+1081x^76+1196x^77+1279x^78+1418x^79+1341x^80+1534x^81+1308x^82+1198x^83+1024x^84+698x^85+563x^86+384x^87+263x^88+162x^89+128x^90+84x^91+51x^92+28x^93+11x^94+14x^95+16x^96+6x^97+7x^98+2x^99+4x^100+1x^102+1x^104+1x^114 The gray image is a code over GF(2) with n=320, k=14 and d=138. This code was found by Heurico 1.16 in 19.8 seconds.