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 1 1 1 2 1 X 1 X 1 1 X^2 1 X X 1 1 X^2+2 1 X 1 1 1 1 1 2 X^2 X 1 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 X X^2+2 X^2+X+2 X^2+X+2 2 X^2 0 X^2+X+2 X^2+X 2 X+2 X X^2+2 X^2 X^2+X X^2+X+2 X^2+X X^2+X+2 X^2+2 X^2 X+2 X X^2 X^2+2 0 2 0 2 X^2+X X+2 2 X^2+2 2 X 0 X^2+X 2 X^2 X 0 X X^2+X X^2+2 0 X 2 X^2+X 0 X^2 X X^2 X^2+2 X X 0 X^2+X X 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 X^2+2 X 2 X X+2 X^2 X X^2 X+2 X^2+X 2 2 X^2+X+2 X^2+X+2 0 0 X^2+X X^2+X 2 2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 0 X^2+X+2 0 X^2 2 X X X 2 0 X^2+X X+2 X^2 X^2 X^2+2 X^2+X+2 X^2+X X^2 2 0 X^2+X X^2+X X^2+X X^2+2 0 X^2+X+2 X+2 X+2 X^2+X X X^2 0 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 0 0 0 0 2 0 2 0 2 2 0 2 0 2 2 0 2 0 2 0 2 0 0 2 0 2 2 0 0 0 2 2 2 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 2 0 2 2 2 2 0 0 0 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 2 0 0 0 0 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 2 2 0 2 0 0 0 0 0 0 0 2 2 2 0 0 2 0 2 2 2 2 0 0 0 2 0 2 0 0 2 0 0 generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+80x^90+222x^91+231x^92+354x^93+431x^94+496x^95+621x^96+488x^97+383x^98+268x^99+201x^100+126x^101+59x^102+60x^103+32x^104+24x^105+1x^106+10x^107+2x^108+4x^110+1x^114+1x^170 The gray image is a code over GF(2) with n=768, k=12 and d=360. This code was found by Heurico 1.16 in 1.55 seconds.