The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 X+2 1 2 1 1 1 2 1 1 1 1 1 X 1 X X 1 1 1 2 1 1 1 0 1 2 1 0 1 1 1 1 0 2 1 X X X 1 1 1 1 1 1 0 1 1 0 2 2 1 X 1 1 0 X+2 1 X 1 X X+2 1 1 1 2 1 1 1 1 1 0 1 1 1 1 X 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 X+2 1 X+2 1 X+3 X+3 0 1 1 1 2 0 X+1 1 X+1 1 1 0 X+2 1 1 3 X X+1 1 3 1 1 1 2 X+1 X+1 X 1 1 X+2 1 1 1 0 X+1 1 X+2 1 X+2 X 0 X 1 1 X X+3 1 1 3 1 1 X+2 1 0 1 1 X+2 X X 1 0 X+2 3 3 2 1 1 X 1 X+1 0 0 0 X 0 X+2 0 X+2 2 X X X 2 0 0 X+2 X X+2 0 2 2 X 2 X X X 0 0 X X+2 0 0 X+2 X 2 X X 0 2 X+2 X 2 X 2 2 X+2 X+2 0 0 X+2 0 X+2 0 0 X 2 2 X+2 X+2 0 2 0 2 X+2 X 2 0 2 0 X+2 X+2 X+2 0 X+2 X+2 0 X+2 X+2 X+2 2 X X+2 0 X X+2 X+2 0 2 X X+2 0 0 0 2 0 0 0 2 2 0 2 2 2 0 0 2 0 2 0 0 2 0 2 2 2 0 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 2 0 0 0 2 2 0 2 0 0 2 0 0 2 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 2 2 0 0 2 2 0 2 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 0 2 2 0 2 2 2 0 2 0 0 2 2 2 0 2 0 0 2 0 0 2 0 0 0 0 0 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 0 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 2 2 0 2 0 2 2 2 0 0 0 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 0 2 0 2 2 2 2 0 0 2 2 2 0 0 2 0 0 2 2 2 0 0 2 0 2 0 0 0 0 2 2 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 2 0 2 2 2 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 0 0 0 2 0 2 2 0 2 0 0 2 2 2 2 2 0 0 2 2 0 2 0 2 2 0 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+72x^81+123x^82+270x^83+216x^84+444x^85+257x^86+386x^87+179x^88+296x^89+307x^90+366x^91+151x^92+382x^93+162x^94+228x^95+65x^96+70x^97+23x^98+18x^99+15x^100+14x^101+13x^102+10x^103+11x^104+2x^105+9x^106+2x^107+1x^108+2x^114+1x^116 The gray image is a code over GF(2) with n=356, k=12 and d=162. This code was found by Heurico 1.16 in 1.79 seconds.