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 X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 X X^2 1 X^2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 X^2+2 X^2+2 X^2+2 X^2 0 X^2+2 0 X^2+2 0 2 X^2+2 X^2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 2 0 2 2 2 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 0 0 2 2 0 2 0 2 2 0 2 2 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 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 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 2 0 0 0 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 0 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 0 0 2 2 2 2 0 0 0 2 generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+68x^86+16x^87+94x^88+176x^89+337x^90+176x^91+78x^92+16x^93+36x^94+17x^96+6x^98+1x^100+1x^106+1x^164 The gray image is a code over GF(2) with n=720, k=10 and d=344. This code was found by Heurico 1.16 in 1.16 seconds.