The generator matrix 1 0 0 0 1 1 1 1 X 1 X 1 X^2+X+2 1 0 2 X+2 X+2 0 X^2+2 1 1 1 1 2 1 1 1 1 1 X^2+X+2 X 1 X^2+X+2 1 1 X^2+X+2 1 1 X^2+X X^2+X 1 X^2+X+2 1 X^2+X 1 1 1 0 1 1 1 1 1 X^2+X+2 1 X^2+2 X^2+2 1 1 1 2 1 X^2+2 1 2 1 X^2+X X^2+X X 2 X^2+2 X 1 X^2+2 2 1 1 X+2 X^2 X^2+X X X^2+X X^2 X^2+X+2 X^2 1 0 1 0 0 0 X^2+3 2 X^2+X+3 1 X^2 X^2 X+3 1 3 1 0 1 X^2+2 1 X^2 3 X^2+1 X+3 0 1 X+2 1 3 X^2+X X^2+X+3 1 1 X^2+X+2 X^2+X+2 2 X+2 1 0 X X^2+X+2 X X^2+3 1 X^2+X+1 1 2 X+1 0 1 3 X^2 X+1 X^2+X+3 X^2+X 1 X+3 X+2 X^2 X+2 X+3 X^2+2 1 X^2+X+2 X X+1 1 X^2+3 X^2 1 X 1 X+2 1 2 1 1 X^2+X+2 X^2+X+2 X 0 1 1 X^2 1 1 1 X^2+X+3 0 0 1 0 X^2 X^2+2 X^2+3 1 X^2+X+3 X^2+3 1 X^2+X X+2 X+1 X^2+1 X^2+X+2 X^2+1 1 X+2 1 2 1 1 1 X 2 X 3 X+2 X^2 3 X^2 X+2 X^2+2 X^2+X+3 0 1 X^2+X+1 3 1 1 X^2+X+1 X^2 X^2+X 2 X+2 X+1 X X+1 X^2+X+2 1 0 X+1 X^2+1 X^2+X X^2+X+3 1 X^2+X+2 X^2+3 X+1 0 X+3 X^2+X+3 1 X^2+1 X^2+X+1 0 0 3 1 0 1 X^2+2 X^2+X X^2 X^2+2 2 1 1 1 X+3 X^2 X^2+X X^2+3 X^2+1 X^2+3 X 0 0 0 1 X^2+X+1 X+3 X+1 X^2+X+3 X+2 X^2+X+2 X+3 X^2+X X^2+3 2 X+3 1 X^2+X X^2+1 X^2+X+2 X+2 X X^2+2 X^2+3 1 X^2+3 X+3 X^2+X+1 X^2+X 0 X X^2+X+1 X^2+2 X+2 1 X^2+X X^2+3 X^2+1 3 2 X+1 X^2+X 1 X^2+3 X+1 X 3 X+1 X^2 X^2+2 X^2 2 X^2+3 2 1 0 1 X^2+X+2 1 X+3 X^2+X+2 X+3 X+1 X+3 X+3 X^2+X+2 X+2 X^2+2 1 X^2 X+3 X+1 0 X+3 X+2 X X^2+X+3 X^2 X+2 3 1 3 3 1 X^2+1 X^2+X+3 X^2 X 0 0 0 0 2 2 2 2 0 0 2 0 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 0 0 0 2 0 0 2 0 2 2 2 2 0 2 0 0 0 2 0 0 2 2 2 2 0 2 0 2 0 2 0 0 2 0 0 0 2 2 2 2 2 2 0 2 0 0 2 0 0 0 0 0 2 0 2 0 0 0 2 2 generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+488x^79+1852x^80+3710x^81+5759x^82+8324x^83+10744x^84+12442x^85+15044x^86+14354x^87+15200x^88+12954x^89+11281x^90+7962x^91+4837x^92+3106x^93+1638x^94+700x^95+341x^96+162x^97+100x^98+36x^99+17x^100+8x^101+4x^103+2x^105+2x^106+2x^107+2x^111 The gray image is a code over GF(2) with n=696, k=17 and d=316. This code was found by Heurico 1.16 in 200 seconds.