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 1 1 X^2 1 1 1 X^2 1 X^2 1 0 X X^2+2 X^2+X 0 X^2+X X^2+2 X+2 X^2+X 0 X+2 X^2+2 2 X+2 X^2 X^2+X X^2+X+2 0 X^2+2 X+2 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 0 X^2+X X^2+2 X+2 X^2 X^2+X+2 0 X 2 X^2+X X^2 X+2 2 X^2+X+2 X^2+2 X 0 X^2+X 2 X^2+X+2 2 X^2+X 0 X^2+X+2 X^2+2 X^2+2 X^2 X^2 X+2 X+2 X X 0 X^2+X 0 2 2 X^2+X X^2+X+2 X^2+X+2 0 2 X^2+X X^2+X+2 2 X^2+X X^2+2 0 X^2+2 X+2 X^2+2 X^2+X+2 X^2+2 0 0 0 2 0 0 0 2 0 2 0 2 2 0 2 2 0 2 0 2 0 0 2 2 2 2 0 0 0 2 2 0 2 0 0 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 2 2 2 2 2 0 0 2 2 0 0 0 2 2 0 0 0 0 0 2 2 0 2 2 2 0 0 0 0 2 2 2 0 2 2 0 0 0 0 2 0 0 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 2 0 0 0 2 2 0 2 0 2 2 0 2 0 0 2 2 0 0 2 0 0 2 2 0 2 2 0 0 2 0 2 0 2 2 2 0 2 0 0 2 2 2 0 2 2 0 0 0 0 2 2 0 0 0 0 0 0 2 0 2 2 2 0 0 2 2 2 0 2 0 2 0 2 0 2 2 0 0 0 2 2 2 2 0 0 2 0 0 0 2 2 0 2 2 0 0 2 0 2 2 0 0 2 0 0 2 0 2 2 0 2 0 2 2 0 0 2 2 2 0 0 2 0 0 2 2 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 0 0 0 2 0 0 0 2 0 0 2 2 2 2 0 2 0 2 2 0 2 0 0 0 2 2 2 0 2 0 2 2 0 0 2 0 2 0 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+74x^81+50x^82+220x^83+63x^84+352x^85+553x^86+344x^87+53x^88+212x^89+34x^90+76x^91+9x^92+2x^94+2x^96+2x^97+1x^166 The gray image is a code over GF(2) with n=688, k=11 and d=324. This code was found by Heurico 1.16 in 0.859 seconds.