The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 1 0 1 1 X^2+X X^2+2 1 1 1 1 X+2 1 1 0 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 0 1 X^2+X 1 1 X^2+2 1 1 1 1 X+2 1 1 0 1 1 X^2+X 1 1 1 0 1 X^2+X 1 1 2 1 1 X^2+X+2 X^2+2 1 1 2 1 1 1 1 1 X^2 X^2+X+2 0 1 2 1 1 1 1 X+2 1 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 1 3 X+1 0 1 X^2+X X^2+1 1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 3 1 X+2 X^2+X 1 X+1 1 0 X^2+1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 0 X+1 1 X^2+1 X^2+3 X^2+3 1 X^2+X 1 X^2+X+2 X^2+X 1 2 X+3 1 1 X^2+2 X^2+X+3 1 X^2+2 3 X^2 X+3 X^2+1 1 1 1 X^2+X+1 1 X^2+X+2 X^2+X X^2+X+3 X+2 1 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 2 0 0 2 0 2 2 0 0 2 0 0 0 2 2 2 2 0 0 2 2 2 0 0 0 2 2 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 0 2 2 0 2 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 0 2 0 2 0 0 2 2 0 2 2 0 2 0 0 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 2 0 2 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 2 0 0 2 2 0 0 0 0 0 2 0 2 0 2 0 2 2 2 0 2 2 0 2 0 0 0 2 2 0 0 0 2 0 2 2 2 2 generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+200x^81+438x^82+376x^83+283x^84+512x^85+474x^86+512x^87+290x^88+376x^89+428x^90+200x^91+2x^94+1x^96+2x^114+1x^116 The gray image is a code over GF(2) with n=688, k=12 and d=324. This code was found by Heurico 1.16 in 0.734 seconds.