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 2 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 0 1 X 1 X 1 X X 0 1 X 2 2 X 1 2 X^2 1 X^2 X X X 0 X 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+X X^2 X^2 X^2+X X+2 0 X^2+X+2 X^2+2 X X^2 X^2+X+2 2 X^2 X^2+2 0 X+2 X+2 2 X+2 X^2+X X^2 X^2 X X^2+X+2 0 X^2+X 2 0 X^2+X X^2+X+2 X 2 X^2+X+2 X 0 X X^2+X+2 X X^2+2 X^2 X^2+2 X+2 X^2+2 X^2+2 X^2+X+2 2 2 X 0 X+2 X^2 0 X X+2 0 X^2+2 X X X+2 X X^2+2 X+2 2 X^2 X X+2 X X^2+X+2 X^2+X 2 X^2 X^2+X 2 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 0 X^2+X 2 2 X^2+X X+2 X^2+2 X^2+X X X^2+2 X^2+2 0 X^2+X+2 X^2+X+2 X 0 0 X^2 X^2+X X^2+X+2 2 0 X^2+X X^2+X+2 2 X^2 0 X 2 X^2 X+2 X^2 X X+2 X^2+2 X+2 X^2+X X^2+2 X^2+2 X+2 X^2+2 X X X^2+2 X^2+X+2 X^2+X+2 X+2 X X^2 X X X^2+2 X^2+X X+2 X^2+X+2 0 X^2 2 X^2+2 X X X^2 X X^2+X X+2 X^2+2 0 X^2+2 X X X^2+X X 0 0 0 2 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 0 0 2 2 2 2 2 0 0 0 0 2 2 0 2 2 2 2 0 2 0 0 0 2 2 2 2 0 0 2 0 2 2 2 0 0 0 0 0 2 0 2 0 0 2 2 0 0 0 2 2 0 0 2 0 0 0 2 2 0 2 2 0 0 2 0 2 0 2 0 0 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 2 0 2 0 0 0 0 0 2 0 2 2 0 0 2 2 2 2 2 0 0 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 2 2 2 2 2 2 2 0 0 2 0 2 0 2 2 2 2 2 0 2 2 0 2 0 0 0 generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 91. Homogenous weight enumerator: w(x)=1x^0+112x^91+234x^92+344x^93+411x^94+312x^95+514x^96+348x^97+601x^98+308x^99+308x^100+168x^101+153x^102+144x^103+52x^104+28x^105+15x^106+20x^107+9x^108+8x^109+4x^110+1x^116+1x^152 The gray image is a code over GF(2) with n=776, k=12 and d=364. This code was found by Heurico 1.16 in 1.58 seconds.