The generator matrix 1 0 1 1 1 X+2 2 1 1 1 1 0 0 1 1 1 X 1 1 0 1 0 1 X 1 1 1 1 1 X 1 1 2 X+2 1 1 1 X 1 X 1 X 1 1 1 2 1 2 1 0 1 2 1 0 1 1 X+2 1 0 1 1 0 2 0 1 1 X 1 2 1 0 1 1 1 1 X 1 2 1 X 0 1 2 1 X X 1 0 1 1 0 1 1 1 0 X+1 2 X+1 1 1 X+3 2 1 1 0 0 1 X+3 1 X+2 1 X+1 X 1 X+2 3 1 X+2 X+1 1 1 X+3 X 1 1 0 1 X+2 1 X+3 2 1 1 3 1 X+2 1 3 1 X 1 X+3 2 1 X+1 1 X+3 2 1 1 1 X+1 0 1 X+1 1 3 1 3 X+1 3 X+1 1 0 1 X 1 1 0 0 1 1 0 X+1 0 0 X 0 0 0 0 X+2 2 X X+2 X+2 0 0 2 2 0 2 X+2 X+2 X X+2 X+2 X X X 2 2 X X+2 0 X X X+2 X+2 2 X+2 X X+2 2 X+2 0 0 X+2 0 0 X+2 0 2 X+2 0 0 X+2 2 0 2 2 X+2 X 0 2 X+2 2 X+2 0 2 X+2 X X+2 2 X X+2 X X 2 0 X X 0 X+2 2 X+2 0 0 2 2 0 0 0 0 X 0 0 0 0 X+2 X X X+2 X+2 X 0 2 X X+2 2 0 X 2 X+2 X+2 2 X+2 X X+2 X+2 2 X+2 X+2 X 2 0 2 0 X+2 0 2 X X+2 X+2 0 X X+2 X 2 0 2 X X+2 X+2 0 X+2 0 X+2 0 X+2 X X+2 X+2 2 X+2 2 0 X 2 X 0 X X 2 X 0 2 X X+2 0 2 0 X X X+2 2 X+2 X 0 0 0 0 X 0 X+2 X X+2 X+2 2 0 X+2 0 X 0 2 X 2 X+2 X+2 0 2 X X X+2 2 0 X 0 X 2 2 X 2 X X+2 X+2 X X+2 0 X X 2 2 2 2 X+2 X X X X+2 X+2 2 X+2 2 X 2 X X+2 0 2 2 X X 2 X+2 2 0 0 X+2 X+2 X 0 0 0 X 0 X X+2 X+2 X X 2 X+2 X X 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 2 2 2 2 0 2 0 2 0 2 2 0 2 0 0 0 2 2 0 2 2 0 0 2 2 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 0 2 0 0 0 2 2 2 0 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 78. Homogenous weight enumerator: w(x)=1x^0+137x^78+76x^79+378x^80+260x^81+588x^82+460x^83+872x^84+456x^85+757x^86+540x^87+713x^88+560x^89+626x^90+404x^91+486x^92+184x^93+285x^94+120x^95+108x^96+12x^97+68x^98+46x^100+27x^102+15x^104+6x^106+3x^108+2x^110+1x^112+1x^124 The gray image is a code over GF(2) with n=348, k=13 and d=156. This code was found by Heurico 1.16 in 6.73 seconds.