The generator matrix 1 0 0 1 1 1 X X+2 1 1 1 X+2 1 X^2+2 1 1 X 1 X^2+X 1 X+2 1 X^2+X+2 1 X^2+2 X^2 1 1 1 X+2 1 X^2+X 1 X^2 1 1 X^2+2 0 1 1 1 X+2 X^2+X X^2+X+2 1 X^2+X+2 1 0 1 1 X^2 1 2 X^2+X+2 X X+2 1 1 1 2 X 1 1 1 X^2+X+2 1 1 X+2 X^2+X 1 X^2 1 1 1 1 1 1 X^2 1 1 X^2+X X^2+2 1 1 1 X+2 X^2+2 X^2+X+2 1 X^2+X X^2+X+2 X+2 1 0 1 0 0 X^2+1 X+1 1 2 0 2 X+3 1 1 1 X 0 1 X^2+1 1 X^2+3 X X^2 1 X^2+X+1 1 X^2+X X^2+X+2 X+3 3 1 X+2 1 X^2+X+2 X X^2+3 1 1 1 X^2 X+3 X+2 1 X^2+2 X^2+2 X^2+X 1 X+1 1 0 1 1 X^2+X X^2+X 1 1 X^2+X X^2+X X^2+X+1 X^2 1 X+2 0 X^2+X+1 X^2+X X^2+X+2 X+1 X^2+X+1 0 1 X^2+X+2 1 X^2+3 X^2+X X^2+X X+2 3 X^2+X+2 1 X+1 2 1 X^2+2 X+3 3 X^2 1 1 1 X X 1 1 2 0 0 1 1 1 0 X^2+1 1 X X^2+X+3 1 X X^2+X X+3 X^2+X+1 X^2+X X+3 X^2 X^2+X X^2+3 1 X+1 1 0 X^2 1 X^2+X+2 X^2+1 X^2+2 X+3 X+3 X^2+2 2 1 X^2+X+1 X^2+X+2 1 X+2 X^2+3 X^2+X+2 X^2+X 2 1 1 X^2+X+3 X^2+X+2 3 X+3 X^2+X+3 X^2+X+3 3 2 1 X^2 3 1 X^2+3 X^2+2 X^2 X^2+X+2 1 X^2 X^2+X+3 3 1 3 X^2+1 1 X^2+1 X^2+3 X 0 2 X^2+X X^2+1 1 2 X^2+X X+3 X+1 X^2+X 1 X X^2+X+2 X^2+3 X^2+X+2 X^2+2 X^2+2 X^2 1 X^2+X+3 0 X 0 0 0 X X+2 2 X+2 X+2 X+2 X 0 X X+2 2 X 2 X^2+X+2 2 2 X^2+2 X^2+X+2 X^2 0 X^2+X X+2 X^2+2 X^2+X+2 X+2 X 0 X^2+2 X^2+X+2 X X^2+X X^2+X+2 X^2 X X^2 X^2 X 2 2 2 X^2+X+2 0 X^2+X+2 X^2+X+2 X X^2+X 2 X^2 X^2+2 0 X^2+2 X^2+X+2 X^2+2 X^2+X+2 X+2 X+2 X^2+X+2 2 X^2+2 2 X X+2 X^2+2 2 X^2 X^2 2 X^2+X+2 X^2+X X^2+X+2 X^2+2 X^2 X+2 X^2+X 2 0 2 X^2+2 X^2 X^2+X 0 X^2+X X^2+2 X^2+X X+2 X+2 X^2 X 0 X^2+X+2 generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+227x^86+940x^87+1636x^88+2418x^89+3005x^90+3474x^91+3249x^92+3824x^93+3400x^94+3062x^95+2483x^96+1980x^97+1240x^98+878x^99+425x^100+196x^101+123x^102+78x^103+56x^104+26x^105+20x^106+16x^107+4x^108+4x^109+2x^112+1x^114 The gray image is a code over GF(2) with n=744, k=15 and d=344. This code was found by Heurico 1.16 in 15.1 seconds.