The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 X X X^2 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 2 0 2 2 0 0 2 0 2 2 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 2 2 2 2 2 0 2 0 2 0 0 2 2 0 2 2 2 0 0 2 0 0 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 2 0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 2 2 2 0 0 0 0 2 2 2 0 2 2 2 0 2 2 0 2 2 0 2 0 0 2 0 2 0 0 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 0 0 0 2 2 2 2 2 2 0 0 0 0 2 2 0 0 2 2 2 0 0 2 2 0 2 0 2 2 2 0 2 0 2 0 0 2 2 0 2 0 0 2 0 2 2 0 2 2 2 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 0 2 0 2 0 2 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 0 0 0 2 2 0 0 2 0 2 2 2 0 0 0 0 0 2 0 0 2 0 2 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 0 0 2 0 2 2 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 2 2 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 2 2 0 2 2 2 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 0 2 2 2 2 0 0 2 0 2 2 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 0 2 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 2 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 2 2 0 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 2 2 2 0 0 0 2 0 2 0 2 2 0 2 0 generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+112x^80+48x^82+256x^85+1184x^86+256x^87+94x^88+48x^90+46x^96+2x^104+1x^160 The gray image is a code over GF(2) with n=688, k=11 and d=320. This code was found by Heurico 1.16 in 8 seconds.