The generator matrix 1 0 0 1 1 1 X 1 X+2 1 1 2 1 X+2 1 1 1 X+2 1 X+2 X+2 1 1 1 0 X+2 1 2 1 1 1 2 2 1 2 X X+2 0 1 1 X+2 1 1 1 0 2 1 0 1 1 1 2 1 2 1 X 1 0 X 1 1 1 2 2 1 2 1 1 1 1 1 2 1 1 1 2 X+2 1 2 1 1 X+2 1 X+2 1 1 0 1 0 0 1 X+3 1 2 0 2 X+1 1 3 1 2 X+1 2 1 3 1 X+2 X 1 X+3 1 1 2 X X+1 X X+2 1 X+2 1 1 1 0 1 X X X+2 X+1 0 3 1 X X 1 X+2 2 3 2 X+3 0 1 1 X 1 1 X+1 X X 0 2 X+2 1 X+1 X+1 2 X+2 0 1 1 X X 0 1 X+2 1 X+1 3 1 1 X+2 X+3 X+1 0 0 1 1 X+1 0 1 X+1 1 X 3 3 2 0 0 X+3 X+1 X+3 0 X 1 X+2 X+2 1 1 2 1 1 X 1 2 X+3 1 3 2 X 1 X+1 1 X+3 1 X X+1 0 2 1 2 3 X+2 2 0 1 1 1 X+2 1 X 1 0 X+2 X+1 0 1 1 1 X+2 1 X+1 3 1 X+2 3 0 X 0 1 2 X+2 3 X+2 X+2 0 X+1 1 X+2 X 0 0 0 X X X+2 2 X+2 0 0 X 0 X 0 X 2 0 X+2 2 X+2 X+2 X+2 X+2 2 X X+2 2 X 0 0 2 X+2 X X X X+2 X+2 2 X 0 2 0 X+2 0 2 2 X+2 2 X+2 2 X+2 2 0 0 0 X X X 2 X 0 X X X X 0 X+2 2 0 0 0 X+2 2 2 X+2 X+2 X 2 X+2 2 X X+2 0 X+2 X+2 2 0 0 0 0 2 0 0 2 2 2 0 2 2 2 0 2 2 2 2 0 2 2 0 0 2 0 2 2 0 0 2 0 0 2 2 2 0 2 0 0 2 0 0 0 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 0 2 2 2 0 0 2 0 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 2 2 2 0 0 2 0 2 2 0 2 2 0 2 0 2 2 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 0 0 0 2 2 2 0 0 2 2 0 2 0 2 0 2 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+166x^78+296x^79+449x^80+480x^81+598x^82+752x^83+660x^84+600x^85+636x^86+612x^87+563x^88+544x^89+424x^90+472x^91+263x^92+204x^93+152x^94+108x^95+88x^96+24x^97+56x^98+16x^100+4x^101+14x^102+3x^104+2x^106+5x^108 The gray image is a code over GF(2) with n=344, k=13 and d=156. This code was found by Heurico 1.16 in 5.22 seconds.