The generator matrix 1 0 1 1 1 X+2 1 1 2 1 1 X 1 1 2 X+2 1 1 1 2 1 1 X 1 1 X+2 1 1 0 1 1 1 X 1 1 1 1 1 X 1 X 1 1 X 1 1 1 1 1 1 X+2 1 1 1 1 X 1 1 X 1 2 1 X 0 1 1 1 1 X+2 1 1 X X 1 1 0 1 1 1 2 1 1 2 1 1 1 X+2 0 1 1 0 X+3 1 X+1 X+2 1 1 X 1 3 2 1 1 1 X+2 X+3 1 0 2 1 X+3 X 1 X+1 2 1 3 0 X+1 1 3 0 X+1 3 2 1 X+1 1 X 1 1 2 X+2 3 X+1 3 2 1 2 X+3 3 X+2 1 X+1 3 1 X+2 1 X+3 X+2 1 X+1 2 X X 1 3 0 1 1 2 X+3 1 2 X X 1 X+3 X+1 1 X+2 X+2 3 1 0 0 X 0 X+2 0 2 2 2 2 0 0 0 X X+2 X+2 X X X+2 X+2 X+2 X+2 X+2 0 X 2 X X 0 2 0 2 0 X 2 X X+2 0 X+2 X+2 X+2 X X X 0 2 X+2 0 X 0 2 X+2 X+2 0 0 X+2 2 X 0 X+2 X 2 X+2 X+2 2 0 X+2 2 X+2 2 X+2 X X+2 X X X 2 X+2 2 X 0 2 2 X X+2 0 0 0 0 0 X 0 0 0 2 X X+2 X X+2 2 2 2 X+2 X X X X+2 0 X+2 0 X 0 2 X X 2 X+2 X 0 X X+2 X+2 2 X 0 X X+2 0 X+2 2 X X X X 0 0 2 X 2 2 0 X+2 0 X 0 0 X X+2 2 X+2 0 0 2 2 2 2 0 2 X+2 X 0 X X+2 X X+2 X+2 0 X X+2 X X 0 X+2 X+2 0 0 0 0 2 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 0 2 2 2 2 2 0 0 2 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 0 0 2 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 0 2 0 2 2 2 2 0 0 0 2 0 2 0 2 0 2 2 0 0 2 2 0 2 0 0 0 2 2 2 0 2 0 0 0 0 2 2 0 0 2 2 0 0 2 2 2 0 0 2 0 0 2 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+262x^80+92x^81+418x^82+156x^83+483x^84+176x^85+472x^86+184x^87+449x^88+172x^89+384x^90+156x^91+286x^92+72x^93+160x^94+16x^95+81x^96+26x^98+29x^100+8x^102+4x^104+4x^106+2x^108+2x^112+1x^120 The gray image is a code over GF(2) with n=348, k=12 and d=160. This code was found by Heurico 1.16 in 10.4 seconds.