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 0 1 X X 1 1 1 1 1 1 1 X 1 0 1 1 1 1 1 1 X 1 2 1 X 1 0 1 X 1 X 1 X 2 0 1 X 1 X 1 2 1 1 2 1 X 0 X 0 X 0 0 X X+2 0 2 X+2 X 0 X X 2 2 0 X X+2 0 0 X+2 X+2 2 X+2 X 2 2 X X 0 X+2 0 2 2 X X 2 X 0 2 0 X X+2 X+2 0 X 2 0 0 X+2 2 X X+2 2 X+2 X 0 X+2 2 X 2 0 X X+2 2 X+2 2 X 0 X+2 X X+2 2 X X X X 0 0 0 0 X X 0 X+2 X 0 2 X 0 X 0 X+2 2 X+2 X 0 X 2 X+2 0 2 X 2 X 2 0 X X+2 2 X+2 0 X X X 0 X X X+2 0 X X+2 X X+2 X+2 X+2 X X 2 X+2 X 0 2 2 X X+2 X+2 X 0 X+2 0 X X+2 X 2 0 X X X+2 2 X+2 2 X+2 X+2 X+2 0 X X 0 X+2 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 2 2 2 0 2 2 0 2 0 2 2 2 0 0 2 0 2 0 2 0 2 0 2 0 0 2 0 2 2 2 2 2 2 2 2 0 2 2 2 2 0 0 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 0 0 2 2 2 2 2 0 2 0 2 0 2 2 0 0 0 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 0 2 2 2 0 2 2 0 0 2 2 0 2 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 2 0 2 0 0 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 0 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 0 2 0 2 2 0 0 2 0 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 0 2 0 2 2 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 0 2 2 2 2 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 2 0 0 2 0 0 2 2 2 0 0 0 2 0 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 2 0 2 0 0 2 0 2 2 0 0 2 2 0 2 2 0 0 2 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 0 0 0 0 2 0 0 0 2 0 2 2 2 0 2 0 2 2 2 0 2 2 0 0 0 0 0 2 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+142x^72+4x^73+234x^74+36x^75+414x^76+132x^77+368x^78+212x^79+435x^80+252x^81+432x^82+236x^83+385x^84+108x^85+260x^86+28x^87+187x^88+16x^89+92x^90+78x^92+18x^94+10x^96+2x^98+9x^100+2x^102+1x^104+1x^108+1x^124 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 2.03 seconds.