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 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 1 0 2 1 0 1 1 X^2+X X^2+X+2 1 1 1 1 1 X+2 2 1 X X^2 X X 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^2+X+2 0 X 2 X^2 X^2+X 2 X^2+X+2 X^2 X^2+X+2 X^2 X+2 2 X^2+2 X^2+2 X^2+X X+2 0 X+1 X+1 1 1 X^2+X+2 1 X+3 X+2 1 1 X+3 X+2 X^2+1 X^2+3 X^2+2 1 X X 1 1 0 X^2+X 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 2 2 2 2 0 2 0 0 0 0 2 0 0 0 2 2 0 0 0 2 0 2 2 2 2 2 0 2 0 0 0 0 0 2 0 2 2 0 2 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 2 2 0 2 0 0 2 0 2 2 0 0 2 0 2 0 2 0 0 0 2 2 0 0 2 0 0 0 2 2 0 2 0 2 0 2 0 2 0 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 2 0 2 0 0 0 2 2 2 0 0 0 0 2 0 2 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 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 2 2 2 0 0 2 2 2 0 2 0 0 2 0 0 0 0 2 0 2 2 2 0 2 0 2 0 0 2 0 0 0 2 2 0 0 2 0 2 0 generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+298x^84+224x^85+528x^86+240x^87+506x^88+608x^89+488x^90+256x^91+411x^92+192x^93+224x^94+16x^95+91x^96+8x^98+2x^100+2x^120+1x^124 The gray image is a code over GF(2) with n=712, k=12 and d=336. This code was found by Heurico 1.16 in 0.797 seconds.