The generator matrix 1 0 0 1 1 1 X X+2 1 1 1 2 1 X^2+X+2 1 2 1 1 1 X+2 X 1 0 0 X^2+2 1 1 1 1 1 X^2+X X 1 X^2 1 1 1 X X^2 1 1 2 1 1 1 X^2+X 1 X^2 1 X^2+X X^2+X+2 1 1 0 1 1 0 1 1 1 0 2 X^2 1 1 1 1 1 X+2 1 1 0 X+2 X^2+X X 1 1 1 X^2 X^2+X+2 1 1 1 1 1 1 X^2 X^2+X+2 X+2 1 X^2 1 1 X^2+2 1 1 1 0 1 0 0 X^2+1 X+1 1 2 2 0 X+3 1 1 1 X^2+X 1 X+1 0 1 X^2 1 X^2 X^2+2 1 1 X^2+X+3 X+1 X^2+X+2 X^2+X X^2+X 1 1 1 X+2 X^2+X+1 X X 1 X+2 1 X^2+X+2 X^2+X X+1 X^2+1 X+2 1 X 1 X^2+X+3 1 X+2 X^2+3 X^2+X+2 1 2 X^2+X+1 1 X+3 X^2+1 X^2 1 2 X^2+X X^2 X 3 3 3 1 X^2+X 0 1 1 1 1 X+3 2 X^2+X 1 1 0 X^2 X+1 X^2+2 X^2+X 3 1 1 X X+2 1 X^2+X+1 3 0 X+1 X^2+2 0 0 0 1 1 1 0 X^2+1 1 X^2+X X+3 X^2+X+1 X^2+3 0 2 2 X^2+X X+2 X^2+1 X^2+1 1 X^2+X+1 X 1 1 2 X^2+X+1 X^2 X+3 X^2+1 2 1 X^2 X 1 3 X^2+X 1 X^2+X+3 1 X^2+X X^2+3 1 X^2 X+1 X+2 X X^2+X+3 X+3 X^2+X+1 0 1 X^2+X+1 X^2+X+2 X^2+X+3 X^2+X+3 1 X+2 X^2 0 X^2+2 X^2+2 1 1 X^2+X X^2+X+1 X^2 X^2+X+2 X+1 X^2+X+1 0 3 X^2+2 X^2+X+2 3 3 X^2+1 X+3 X^2+1 X 3 X+3 0 X+2 1 X^2+X+1 X^2+X+1 X+1 2 1 X^2+X X^2+X+2 X^2+X X^2+3 1 X+1 X^2+2 X^2 0 0 0 X X+2 2 X+2 X+2 X^2+2 X^2 0 2 X X+2 X^2+2 X^2 X^2 2 X^2 2 2 X^2+X X^2+X X^2+X+2 X^2+X X X 0 X X+2 0 0 X^2+2 X^2+2 2 X^2 0 X X^2+X X X^2 X X^2+2 X^2+X+2 0 2 X X^2+2 X^2+X+2 X^2+X X^2+X+2 0 X+2 X^2+X+2 X+2 X+2 X X^2+X+2 X^2 X X^2+2 X^2+2 0 2 X^2+X 2 X^2+X+2 X+2 X^2+2 X^2+X+2 X^2+X+2 X X+2 X^2 X+2 X^2+X X 0 X^2+X X^2+X+2 X^2+X+2 X^2+X+2 X+2 X^2+X X^2+X X^2 X^2+X+2 X^2 X^2+X X+2 X^2+X X X X X^2+X+2 X^2+X X generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+245x^90+1068x^91+1804x^92+2428x^93+2749x^94+3220x^95+3745x^96+3494x^97+3211x^98+3116x^99+2473x^100+1968x^101+1344x^102+850x^103+490x^104+238x^105+111x^106+84x^107+55x^108+24x^109+3x^110+14x^111+14x^112+8x^113+9x^114+2x^116 The gray image is a code over GF(2) with n=776, k=15 and d=360. This code was found by Heurico 1.16 in 16.1 seconds.