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 X 1 1 1 1 1 1 X^2 1 1 X 1 X 1 0 X^2+2 0 X^2 0 0 X^2 X^2+2 2 0 X^2+2 X^2+2 2 0 X^2 X^2 0 X^2 X^2+2 0 X^2+2 2 0 X^2+2 0 X^2 X^2 0 2 X^2 0 X^2+2 2 X^2 X^2+2 2 2 X^2 X^2 0 2 X^2+2 0 X^2+2 2 2 X^2 X^2+2 X^2+2 0 0 X^2+2 X^2+2 0 X^2 2 X^2+2 X^2 2 X^2 2 0 X^2+2 2 2 0 X^2+2 2 0 X^2 X^2+2 0 X^2 0 0 2 X^2+2 X^2 2 X^2+2 2 2 X^2+2 X^2 X^2 2 0 0 X^2+2 X^2 0 X^2+2 X^2 0 X^2 0 X^2 2 X^2 0 X^2+2 2 X^2 X^2 2 0 X^2 X^2+2 2 0 0 X^2 0 X^2+2 X^2 X^2+2 2 2 2 2 X^2+2 0 X^2+2 0 X^2 X^2 0 X^2+2 X^2+2 0 2 X^2 X^2+2 0 X^2+2 2 X^2 0 X^2+2 2 0 X^2+2 0 2 X^2+2 X^2 0 2 X^2+2 X^2+2 2 X^2+2 X^2 0 X^2+2 X^2+2 X^2+2 2 X^2 X^2 2 X^2 X^2 X^2+2 0 2 0 X^2+2 0 X^2+2 X^2+2 X^2 0 0 0 2 0 0 2 0 2 2 0 2 2 2 0 2 0 0 2 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 2 0 0 0 2 2 0 2 0 2 0 2 0 2 2 2 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 0 2 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 0 2 2 0 2 0 0 0 2 2 0 0 2 2 2 0 2 0 2 0 2 2 0 0 0 0 0 2 0 0 2 0 2 0 0 2 0 2 2 0 0 0 0 0 2 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 0 0 0 0 0 0 2 2 2 0 2 2 2 0 2 2 2 0 0 2 2 0 2 2 0 0 2 0 2 0 0 0 2 0 2 2 0 0 2 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 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+52x^80+102x^82+32x^83+81x^84+480x^85+582x^86+480x^87+64x^88+32x^89+66x^90+54x^92+18x^94+3x^96+1x^164 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 0.875 seconds.