The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X+2 1 1 0 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 1 X+2 1 1 1 0 X+2 1 1 1 2 1 1 1 X 1 1 1 0 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 2 1 1 1 1 1 1 0 1 X+2 1 X+2 X X+2 1 1 2 1 0 X 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 0 X+2 X+1 1 X+2 X+1 1 0 2 1 3 X+2 X 1 3 X+1 0 1 1 3 X X+3 1 1 0 X+3 1 X+2 0 X+3 1 1 2 X X 3 X+2 2 X+2 2 0 0 X X+2 X+1 3 1 X+1 1 1 X+1 1 X+1 X+3 0 X+2 1 X+1 1 1 1 1 1 3 X+1 1 X+3 X 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 0 2 0 0 2 0 2 2 2 2 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 0 0 2 2 0 0 2 0 0 0 0 0 2 2 0 2 2 2 2 0 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 0 2 0 2 2 0 2 0 2 2 2 2 2 2 2 0 0 0 2 0 0 2 0 0 2 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 2 2 0 0 2 0 0 2 0 2 0 0 0 0 2 0 2 0 2 0 0 0 2 0 2 0 0 2 0 2 0 0 2 2 2 0 0 2 0 0 0 2 2 0 2 0 2 2 2 0 0 0 2 0 2 0 2 2 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 0 2 2 0 2 2 0 0 0 2 0 2 0 2 0 2 0 0 2 2 0 0 2 2 0 0 0 0 0 2 2 2 2 0 2 2 2 2 0 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 0 2 2 2 0 2 2 2 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 0 2 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 2 0 0 0 2 2 0 2 0 2 2 0 0 2 2 0 0 2 2 2 2 2 0 0 0 0 2 2 2 2 0 2 0 0 0 0 2 0 2 2 2 0 0 0 2 0 0 2 0 2 2 0 0 2 2 0 2 0 2 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+85x^80+12x^81+188x^82+156x^83+338x^84+236x^85+330x^86+236x^87+368x^88+244x^89+314x^90+276x^91+380x^92+228x^93+286x^94+100x^95+191x^96+48x^97+34x^98+19x^100+14x^104+5x^108+5x^112+1x^116+1x^124 The gray image is a code over GF(2) with n=356, k=12 and d=160. This code was found by Heurico 1.16 in 1.7 seconds.