The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 X X X 2 1 1 0 0 0 1 1 X 1 0 1 1 X 0 0 1 1 1 1 1 X 1 1 0 1 1 X X 1 X 1 X X 1 X 2 1 1 0 X 0 0 0 0 0 0 2 2 X X+2 X 0 0 2 X+2 X+2 X X X X 0 X X+2 X 0 X X+2 2 X+2 2 2 X+2 X 0 0 X 2 2 X+2 2 X X X 2 2 X X X+2 X X+2 X 0 X+2 X+2 0 2 X+2 X+2 2 0 2 X+2 2 0 2 2 2 2 X 2 0 2 X X+2 0 2 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 2 X+2 X+2 X+2 X X+2 X+2 X 2 2 X+2 X+2 0 0 X X X X+2 X+2 X+2 2 2 X+2 X X 2 2 X X 0 X 2 0 2 0 X 0 X 2 X 2 X+2 X 0 X X X X X+2 2 X+2 X+2 2 2 2 2 X+2 X X 2 2 0 X 2 0 2 0 0 0 0 0 0 X 0 0 2 X+2 X X X X 2 X+2 X 2 2 0 2 2 2 2 2 X X+2 X 2 X X+2 X+2 X X+2 0 2 0 0 0 X+2 2 X X+2 0 0 0 0 X X X+2 X+2 X+2 0 X 2 0 X X X 0 2 0 0 X+2 2 X+2 0 X X 0 X X+2 X 0 2 0 X+2 X+2 X+2 2 0 0 X+2 0 0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X 0 2 X 0 X+2 X+2 X X+2 X 2 2 X 2 2 0 X+2 2 0 X+2 X X+2 2 0 X 0 0 2 0 X X X+2 0 X X X 0 2 X+2 2 0 0 X X+2 X X 2 2 X 0 X+2 X+2 X+2 2 X+2 2 X+2 X 2 X 2 X X+2 X+2 2 0 X+2 0 0 0 0 0 X X 2 X+2 X X+2 2 X X 0 X 0 X+2 X+2 0 X 2 2 X+2 2 X X+2 X+2 2 X 2 2 X+2 0 X X+2 0 0 X X 0 X+2 2 2 X+2 2 2 X+2 X X+2 2 X X+2 X X+2 X+2 2 2 0 X 2 2 0 0 0 0 X 2 X+2 0 2 0 X+2 X X+2 2 X+2 X+2 X+2 2 0 generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+42x^70+122x^71+141x^72+216x^73+279x^74+302x^75+418x^76+460x^77+565x^78+630x^79+661x^80+728x^81+639x^82+638x^83+538x^84+384x^85+353x^86+284x^87+215x^88+138x^89+127x^90+108x^91+50x^92+50x^93+31x^94+20x^95+22x^96+6x^97+11x^98+8x^99+2x^100+2x^101+1x^118 The gray image is a code over GF(2) with n=324, k=13 and d=140. This code was found by Heurico 1.16 in 7.66 seconds.