The generator matrix 1 0 0 1 1 1 0 1 1 2 1 2 1 X+2 1 X+2 1 0 1 X+2 1 1 1 X 1 X X 1 1 X 1 X 1 1 1 0 1 1 1 0 1 0 1 X+2 2 1 0 2 1 X+2 1 2 1 X 1 1 0 1 X+2 X 1 X+2 2 0 2 1 1 X 1 1 1 0 1 1 X+2 1 2 2 0 0 X X 1 1 1 1 X+2 X+2 0 0 1 0 0 1 1 1 2 1 1 3 1 2 2 X+3 1 X X+2 X+2 1 X+1 X+3 X+1 1 0 X+2 1 X+2 X+2 1 1 1 X+3 2 2 0 3 3 0 X+2 X+2 1 X+1 1 1 X+1 1 1 3 1 1 1 X X+2 0 X+2 2 0 1 1 3 1 1 1 X X+3 X+3 1 X+1 X+2 3 1 X+3 X+3 0 X+3 2 1 2 2 1 1 3 X+2 X X 1 0 1 0 0 1 X+1 X+3 0 X+1 X 1 3 X+2 X 3 1 0 2 3 1 2 3 1 X X+1 X 0 1 X+1 X+1 X X X+1 3 0 X+1 1 1 3 0 X+2 1 X+2 2 1 0 2 X 1 X 1 3 X+2 X+2 X+2 1 X+3 3 1 1 X+1 2 3 0 X X 1 X+3 X+3 X+3 X+3 0 0 X+1 2 0 1 0 1 2 1 1 1 1 X 2 0 X+1 X+2 1 0 0 0 0 2 0 0 0 2 2 2 0 0 0 2 2 2 2 2 2 0 2 0 0 2 0 2 2 2 0 0 0 0 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 0 2 0 2 2 2 0 2 2 2 0 2 2 0 0 2 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 0 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 0 2 2 2 0 0 2 2 0 2 2 2 0 2 0 2 0 2 0 2 0 0 2 0 0 0 2 0 0 2 2 0 2 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 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 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 0 2 2 0 2 0 2 0 0 2 2 0 2 2 2 2 0 0 2 0 0 0 2 0 2 2 0 2 0 0 0 0 2 2 0 0 0 2 0 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+96x^82+152x^83+413x^84+328x^85+471x^86+248x^87+454x^88+256x^89+396x^90+212x^91+257x^92+112x^93+182x^94+104x^95+113x^96+52x^97+121x^98+44x^99+29x^100+16x^101+11x^102+8x^103+8x^104+4x^105+2x^106+5x^108+1x^114 The gray image is a code over GF(2) with n=356, k=12 and d=164. This code was found by Heurico 1.16 in 1.38 seconds.