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 2 1 1 X 1 X^2+2 1 X^2+2 1 1 X 1 X 1 X 1 X X 2 1 1 1 X^2 1 1 0 X 0 X 0 2 X+2 X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2 0 X^2+2 X X^2+X+2 X 0 2 X+2 X^2 0 X^2+X X+2 X^2 X^2+X+2 X^2+X 0 X^2 X X+2 0 2 X 0 X X^2+X+2 X^2 2 X^2+2 X X^2+X+2 2 X+2 X^2 X^2+2 X^2+X X^2+X+2 X^2+2 X^2 X^2+X+2 X^2+X X^2+2 X^2 X+2 X 0 2 X^2+X X^2+X+2 0 2 X^2+2 X^2+X+2 X 2 X^2 X X^2+2 X 0 X X^2+X+2 X+2 X^2+X+2 X+2 X^2+X X^2+X X^2+X X+2 X^2 2 X X^2 X^2+2 2 0 0 0 X X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2 X 0 2 X^2+X+2 X+2 X^2 0 X+2 X X^2 X^2+X+2 X X^2+2 X^2+2 X^2 X^2+X X^2+X+2 2 X^2+X X+2 2 2 2 X+2 X^2 X X^2 X^2 X+2 X^2+X+2 X^2+2 X 2 X X^2+X X^2 X^2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 2 2 X X X^2+X X^2+X 2 2 X^2+X+2 X^2+X+2 0 0 0 X^2+X+2 X 2 X^2+2 X 0 X^2+X X^2+X+2 0 X^2 X^2+2 X X^2 X X^2+X+2 0 X^2 0 X^2 X X X^2+X 0 X X^2+X X^2 0 0 0 2 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 2 0 0 2 0 0 2 2 2 0 2 0 2 0 2 2 2 0 2 2 0 0 0 2 0 2 0 2 0 2 0 0 2 2 0 2 0 2 0 2 0 0 2 2 0 2 0 0 0 0 2 0 2 0 0 0 2 0 2 2 2 0 0 2 0 0 0 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 2 2 2 0 0 2 2 2 0 0 0 0 2 0 2 2 0 2 2 2 2 0 0 0 0 2 2 2 0 0 0 0 2 0 2 0 2 2 0 0 2 0 2 0 2 0 2 2 0 2 0 2 0 2 2 0 0 2 2 2 2 0 0 2 0 0 0 0 2 0 2 2 2 0 2 0 generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+68x^85+224x^86+234x^87+351x^88+464x^89+306x^90+964x^91+319x^92+420x^93+196x^94+182x^95+179x^96+52x^97+58x^98+44x^99+13x^100+4x^101+16x^102+1x^160 The gray image is a code over GF(2) with n=728, k=12 and d=340. This code was found by Heurico 1.16 in 1.28 seconds.