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 X 0 1 1 X X^2+2 1 1 X 0 X X^2+2 X X X 2 X X^2 X X X X 2 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 0 1 1 1 1 1 1 X X X^2 1 0 X X^2 2 2 X^2 0 X X^2+2 X^2+X 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X+2 2 X^2+X+2 X^2 X 0 X^2+X X^2+2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X X^2+X X 2 X^2+X+2 X+2 X X^2 X X^2+X X X+2 X 0 X^2+2 X^2+X+2 X X X 2 X^2 X^2+X+2 X X X 0 X^2+2 0 X^2+2 2 X^2 2 X^2 X^2+X X+2 X^2+X+2 X X^2+X X+2 X^2+X+2 X X^2+2 X^2 0 2 X^2+X 0 X^2+X X^2+X+2 2 X^2 X^2+2 2 X^2 0 X^2 X^2 X^2 X^2 0 0 2 2 2 0 0 2 2 2 0 0 0 0 2 2 0 0 2 2 2 2 0 0 2 2 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 2 2 2 0 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 2 2 0 0 0 2 0 0 2 0 2 0 generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+28x^85+205x^86+13x^88+2x^89+2x^92+2x^97+2x^98+1x^110 The gray image is a code over GF(2) with n=688, k=8 and d=340. This code was found by Heurico 1.16 in 31.2 seconds.