The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X+2 1 1 0 1 0 1 1 X+2 1 1 1 0 1 1 2 1 1 X+2 1 X 1 1 1 0 1 2 1 X+2 X+2 1 X 1 1 1 1 1 X+2 X 1 1 1 1 X+2 1 1 1 X+2 1 1 1 1 X 0 2 2 1 1 1 1 1 X X+2 0 X X X 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 X+2 X+1 1 0 0 X+1 1 X+2 3 1 1 0 1 X+2 1 2 X+1 X+2 1 X+2 1 X+3 1 1 X+1 1 X X+1 3 X 0 1 1 3 3 X 0 1 0 3 X 1 2 X X+2 X+3 1 1 X 1 X+2 X 0 2 1 1 1 1 X+2 X+2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 2 2 0 0 2 0 2 2 2 2 0 0 2 2 2 0 0 2 0 0 2 0 2 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 2 2 2 2 0 2 0 0 2 2 2 0 2 2 2 0 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 2 0 2 2 2 0 0 0 2 0 2 0 2 0 0 0 2 2 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 2 2 0 2 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 0 2 0 2 0 0 2 2 0 0 2 2 0 2 0 2 2 2 2 0 2 0 0 2 0 2 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 0 0 2 2 2 0 2 0 2 2 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 0 2 2 2 2 0 0 0 2 0 2 0 0 0 0 2 0 0 2 2 0 2 0 2 0 0 0 2 0 0 2 0 0 2 2 2 2 0 0 2 0 2 2 2 2 0 2 2 0 2 2 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 2 0 2 2 2 0 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 2 0 0 2 0 2 2 2 0 2 2 2 2 0 2 0 2 2 2 0 2 2 2 2 2 0 0 0 generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+84x^72+28x^73+196x^74+108x^75+294x^76+188x^77+341x^78+284x^79+392x^80+324x^81+350x^82+260x^83+368x^84+212x^85+302x^86+116x^87+115x^88+16x^89+74x^90+12x^92+11x^94+4x^96+4x^98+6x^100+2x^102+3x^104+1x^112 The gray image is a code over GF(2) with n=324, k=12 and d=144. This code was found by Heurico 1.16 in 1.44 seconds.