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 1 1 1 X 1 1 1 1 1 0 1 1 1 1 X 1 1 1 0 1 X 1 1 1 0 1 1 1 X 1 X 0 1 0 1 0 1 0 1 1 X 1 1 0 X 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 X+2 0 X+2 X 2 X+2 0 2 X+2 X X+2 X X 0 2 0 2 0 X+2 X+2 0 2 X+2 X 2 2 X+2 X+2 X X+2 2 X X X X 0 X X+2 0 0 0 X X X+2 X+2 2 0 X X+2 X+2 X+2 X+2 0 X+2 X X+2 X X X X X 2 2 X+2 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 0 2 0 2 2 2 0 0 0 2 2 0 0 0 2 2 0 0 0 0 2 0 0 2 2 2 0 0 2 2 2 0 0 0 0 2 2 0 2 0 2 0 2 0 0 2 2 0 2 2 0 2 0 2 0 2 0 0 0 0 2 2 2 0 2 2 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 2 2 0 2 0 2 2 0 0 2 0 2 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 2 0 0 2 2 0 0 2 0 2 2 0 0 0 2 0 2 2 0 2 0 0 0 2 0 2 2 0 2 0 2 0 0 2 0 2 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 2 2 2 2 0 2 0 2 2 0 2 0 0 2 2 0 0 2 0 2 2 2 0 2 0 0 0 0 0 2 0 2 2 0 2 2 2 0 2 2 0 2 0 0 2 0 0 2 0 2 2 2 0 2 2 0 2 2 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 2 0 2 0 2 2 0 0 2 0 0 2 0 2 0 0 2 2 0 0 2 0 2 0 2 2 0 2 2 2 0 2 2 0 0 2 2 2 0 2 0 0 2 0 0 0 0 0 2 0 0 2 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 0 0 2 2 0 2 2 0 2 2 2 2 2 2 0 2 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 0 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 2 2 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 0 0 2 2 0 2 2 2 0 0 0 2 0 0 2 2 2 0 0 2 2 2 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 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+48x^72+132x^74+8x^75+160x^76+48x^77+208x^78+120x^79+238x^80+160x^81+240x^82+120x^83+189x^84+48x^85+139x^86+8x^87+108x^88+42x^90+16x^92+4x^94+3x^96+2x^98+3x^100+1x^102+1x^104+1x^136 The gray image is a code over GF(2) with n=324, k=11 and d=144. This code was found by Heurico 1.16 in 0.822 seconds.