The generator matrix 1 0 0 1 1 1 0 1 1 2 1 X 1 X+2 1 X+2 1 0 1 X+2 1 X 2 X 1 2 1 1 1 X 1 2 1 1 1 X+2 X 1 1 1 1 1 X+2 1 X+2 1 0 1 1 X 2 X 1 2 X 1 2 2 2 X 2 1 1 1 1 1 X X+2 1 0 X+2 X 1 1 1 X+2 1 1 2 1 1 1 X+2 1 1 1 0 1 0 0 1 1 1 2 1 1 X+1 X+2 X 1 X+2 1 X+3 X+2 X+1 1 2 1 1 X+2 2 1 X+2 3 1 1 X+2 1 X+1 X+3 0 0 0 3 0 X+3 X+2 X 0 2 1 1 1 X+2 X+2 1 1 1 X+2 X+2 1 2 0 1 2 1 1 X+2 X+3 2 0 2 2 1 X+3 X X+2 1 X+2 X+2 X 1 X+2 X 1 X+1 X+3 X+2 1 3 3 0 0 0 1 X+1 X+3 0 X+1 X 1 X 0 1 1 1 X 2 X+2 1 3 X+1 1 X+2 1 1 0 2 X+3 X 3 X+1 0 X+3 3 0 2 1 1 X X+1 X+3 X+2 2 1 X+1 X+2 0 X 1 X+3 1 1 1 X+3 1 2 X+2 1 X+3 1 3 2 X+1 1 X+1 3 X+2 1 X+3 X+3 1 1 0 3 2 X X+2 X+1 2 2 2 X+2 X+3 0 2 X 0 0 0 0 2 0 0 0 2 2 0 2 2 0 2 0 2 2 0 2 0 0 0 2 2 0 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 2 0 2 0 0 2 0 0 2 2 0 0 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 2 2 2 0 0 2 2 2 2 0 2 2 0 2 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0 0 2 2 0 0 2 0 2 2 0 2 0 2 0 0 0 0 2 2 0 0 2 2 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 2 2 2 0 2 0 2 0 0 2 0 2 2 2 0 2 0 0 0 0 2 0 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 0 0 2 2 0 2 2 2 2 0 0 2 2 0 2 2 2 2 2 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 0 0 0 0 2 0 2 2 0 2 0 2 0 0 2 0 0 2 0 0 2 2 2 2 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 2 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 2 0 2 2 2 2 2 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+158x^78+268x^79+446x^80+572x^81+657x^82+580x^83+619x^84+752x^85+597x^86+660x^87+581x^88+448x^89+415x^90+424x^91+284x^92+256x^93+170x^94+108x^95+88x^96+20x^97+40x^98+4x^99+20x^100+6x^102+4x^103+8x^104+4x^106+1x^108+1x^110 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 5.18 seconds.