The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 2 1 2 1 X 1 1 X+2 1 1 X 1 1 0 1 X+2 1 1 1 1 2 X 1 X 1 1 X 2 1 1 1 1 1 1 1 X 1 1 X+2 1 1 1 1 1 1 1 2 X X+2 X 1 1 1 1 1 1 1 0 X X+2 1 X+2 1 1 X+2 1 1 1 1 1 1 1 1 2 2 0 1 1 0 X+3 1 X X+3 1 3 1 0 1 X+2 1 1 1 X+2 1 X+2 X+1 1 2 X+1 1 X+2 3 1 X 1 X+3 X+2 X+1 X+2 1 1 X+3 1 1 1 1 1 X X+1 X+1 2 2 0 1 1 X+2 X+1 1 X+1 3 3 X+1 0 2 X+2 1 1 1 1 0 X+3 X+1 X+2 X X 0 1 1 1 X+3 1 X+3 X+3 1 X X+1 2 X+2 0 2 X 1 1 1 0 0 X 0 X+2 0 0 2 2 0 2 X 0 X X+2 X+2 X+2 X+2 X+2 0 0 X X X+2 2 2 X+2 X+2 0 0 X+2 X+2 2 X X 2 0 2 2 2 X 2 X+2 2 X+2 X+2 X 2 0 X 0 X X+2 X 0 X+2 2 2 2 0 0 X X 2 X X+2 X 0 0 X+2 X+2 X+2 0 0 X+2 2 X 2 X 2 0 0 2 X X X X X 0 0 0 0 X 0 0 X X+2 X+2 2 X X X+2 X+2 2 X+2 X 2 2 0 0 X+2 0 X+2 0 0 X X X+2 2 0 2 X X 2 X+2 0 2 X 0 X+2 X+2 0 2 X+2 2 2 2 0 X+2 X+2 X 0 0 X X+2 X+2 X+2 2 X+2 2 2 X X X+2 0 2 0 X+2 X X+2 X+2 2 X+2 2 0 X X 2 X X+2 X 2 X X+2 X+2 X+2 0 X+2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 2 0 0 2 2 2 0 0 0 2 2 2 2 0 0 0 2 2 0 0 2 2 0 2 2 0 2 0 0 0 2 0 0 2 2 0 2 2 0 0 2 2 2 0 0 0 2 2 2 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 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 2 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 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 2 0 2 2 2 0 0 2 2 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 2 0 2 2 2 2 2 0 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 2 0 0 2 0 0 0 2 0 0 0 2 0 2 0 0 0 0 2 2 0 2 0 0 2 0 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+131x^80+88x^81+399x^82+284x^83+599x^84+424x^85+757x^86+484x^87+804x^88+512x^89+763x^90+484x^91+678x^92+424x^93+432x^94+284x^95+298x^96+88x^97+93x^98+66x^100+41x^102+34x^104+9x^106+8x^108+2x^110+2x^112+1x^116+2x^120 The gray image is a code over GF(2) with n=356, k=13 and d=160. This code was found by Heurico 1.16 in 6.37 seconds.