The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 0 1 1 2 X 1 1 X 1 1 2 1 1 X+2 1 1 1 1 1 1 X 1 X X 1 1 2 1 0 1 X 1 1 0 1 1 1 1 1 2 1 2 1 1 X 0 1 1 1 1 1 1 1 X 0 1 1 1 1 0 1 0 1 2 0 1 X+2 0 1 1 X 1 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 X X+1 1 2 3 1 1 X+2 1 1 0 X+3 1 1 X+2 1 3 0 1 X+1 X+1 X 1 2 1 1 X 3 1 X+1 1 X 1 2 X+1 1 2 X+3 2 1 X 1 2 1 X+1 3 1 1 X+2 3 X 3 3 X+3 1 1 1 X 1 2 2 1 0 1 X+1 1 1 X 1 1 X X+3 0 X+3 0 0 X 0 X+2 0 X+2 2 X X X 2 X+2 0 2 X+2 2 X+2 X 0 X+2 2 0 X 0 X 2 0 X+2 2 0 X+2 0 X+2 X+2 X X 2 X 2 X 2 X+2 2 X+2 2 X 2 X 0 0 X 0 X+2 X+2 0 0 2 2 X X+2 X X+2 0 X X X 0 0 X+2 X X 2 X 2 X X+2 X 2 0 2 0 0 0 X+2 X 0 0 0 2 0 0 0 2 2 0 2 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 0 2 2 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 0 0 0 0 2 0 2 2 0 0 2 0 2 2 2 0 0 2 0 2 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 2 0 2 2 2 2 2 2 2 2 0 2 2 0 2 2 0 2 0 0 0 2 0 2 2 0 2 0 0 2 0 0 0 2 0 0 2 2 0 0 0 0 2 2 2 2 0 2 0 2 2 0 2 0 2 0 0 2 2 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 0 0 0 2 0 2 2 0 0 2 0 0 0 2 2 2 0 2 0 0 2 0 2 0 2 0 2 0 2 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 2 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 0 2 2 0 2 2 2 2 0 0 2 0 0 0 2 2 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 0 2 2 2 0 0 0 2 0 2 0 2 0 2 2 0 2 2 2 2 0 0 0 2 2 2 0 2 2 0 2 2 0 2 2 2 2 0 0 2 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+83x^78+112x^79+304x^80+152x^81+394x^82+268x^83+352x^84+208x^85+392x^86+292x^87+370x^88+216x^89+308x^90+212x^91+204x^92+64x^93+71x^94+12x^95+27x^96+18x^98+11x^100+14x^102+8x^104+2x^112+1x^116 The gray image is a code over GF(2) with n=344, k=12 and d=156. This code was found by Heurico 1.16 in 1.64 seconds.