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 1 1 1 1 1 0 1 1 X X 1 1 2 1 1 1 X 1 0 1 X X 1 1 1 X 1 X 1 X X 0 1 2 X 1 1 1 2 1 X X X 0 X 0 0 0 X X+2 X 0 2 2 0 X X+2 X X+2 X+2 X+2 X+2 2 0 0 X+2 2 0 2 X X X+2 2 X+2 X+2 X 2 2 X 0 X X 2 X 2 X 0 2 2 0 2 0 X+2 X X X+2 2 2 X 0 X+2 X+2 X X+2 2 0 0 0 X X X 0 X 0 0 X+2 X 0 X+2 2 X+2 0 0 2 0 0 X 0 X X X+2 0 0 0 X+2 X+2 X X 2 0 X 2 0 X+2 X+2 2 X+2 2 X+2 0 2 2 X+2 X+2 0 0 X+2 2 0 X+2 X+2 2 X+2 0 X 0 2 X X 0 2 X 0 X 2 X+2 2 X X 2 2 X+2 X X+2 X+2 X X X 2 0 0 X X X+2 X+2 0 0 X+2 0 2 0 X 2 2 2 0 0 0 X X 0 X+2 X 2 X+2 X 2 2 X X 2 0 X+2 0 X 2 X X 0 2 X 0 X+2 X X X+2 X+2 2 0 0 X X X 0 2 X+2 2 X+2 0 2 X+2 X 2 X 0 X+2 X 2 0 X X X 0 X+2 0 0 0 0 X X+2 X+2 2 X+2 0 X X+2 X 2 X X 0 X 2 X+2 X 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 2 2 0 0 0 2 2 0 0 2 0 0 0 2 2 2 0 2 2 0 2 0 2 2 2 0 0 0 2 2 2 2 2 0 2 0 2 0 0 2 2 0 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 2 0 0 2 2 2 0 0 0 0 0 2 2 0 2 0 2 0 0 0 0 2 0 2 2 2 2 2 2 2 0 2 0 0 2 2 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 2 0 2 2 2 2 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 0 0 0 0 2 2 0 0 2 2 0 0 0 2 2 0 0 0 2 2 2 0 0 2 2 2 2 2 2 2 2 2 0 0 2 0 2 2 0 2 0 2 0 0 2 2 0 2 2 2 0 0 2 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+108x^72+8x^73+278x^74+44x^75+402x^76+128x^77+340x^78+244x^79+497x^80+216x^81+478x^82+180x^83+340x^84+144x^85+210x^86+44x^87+181x^88+16x^89+102x^90+54x^92+48x^94+12x^96+14x^98+4x^100+2x^102+1x^120 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 1.92 seconds.