The generator matrix 1 0 1 1 1 X+2 1 1 2 1 1 X 1 1 0 X 1 X 1 1 1 0 1 1 1 X+2 1 1 0 1 1 2 1 1 1 1 X X 1 X 1 1 1 1 1 1 X 1 0 1 1 2 1 1 1 2 0 X 2 1 X 1 1 1 1 1 X+2 1 X+2 2 1 1 0 1 2 1 X 0 1 1 1 0 1 1 X+2 X+3 1 0 X+1 1 X 3 1 0 3 1 1 X+2 1 X+1 3 X+1 1 2 X X 1 X+3 X+2 1 1 0 1 X+2 1 3 2 1 1 X+3 1 2 2 X X X 3 1 X 1 3 X+1 1 2 X+3 X+1 1 1 1 1 X+3 1 X+2 3 X+3 X+3 3 1 X+1 1 2 X+1 X 1 X+3 1 3 X+2 1 0 X+2 X+2 0 0 X 0 X+2 0 X+2 0 X+2 X 2 X+2 0 2 0 X 0 2 2 X+2 X+2 X+2 X X 0 2 X X 2 X 0 X+2 2 X+2 0 X 0 X+2 X+2 X X+2 0 X+2 2 2 0 X+2 X+2 0 0 0 2 2 X 2 X+2 2 2 X+2 0 X+2 0 X 0 2 X 2 0 X X X 0 X+2 X 2 X X X+2 X 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 0 2 2 0 0 0 2 0 2 0 2 2 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 0 0 2 0 2 2 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 0 2 2 2 2 2 2 0 0 2 0 2 2 2 0 2 0 2 2 0 2 2 0 2 2 2 2 2 0 0 2 2 0 0 0 2 2 0 2 2 0 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 2 0 2 0 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 2 0 2 0 2 0 2 0 0 0 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 2 0 0 2 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 2 2 2 2 2 0 0 2 2 0 2 0 0 2 0 2 2 2 0 0 2 0 2 2 0 0 0 2 2 2 0 2 0 2 0 0 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 0 0 2 2 0 0 0 0 0 2 2 2 0 0 0 2 0 2 2 0 2 2 0 2 2 2 2 0 0 2 0 0 0 0 0 0 2 2 2 0 2 0 2 0 0 2 2 0 0 2 2 2 2 2 0 2 0 0 2 0 0 2 2 0 0 2 2 0 0 2 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+160x^72+76x^73+362x^74+224x^75+579x^76+424x^77+744x^78+528x^79+817x^80+576x^81+746x^82+528x^83+730x^84+408x^85+432x^86+240x^87+297x^88+52x^89+118x^90+16x^91+72x^92+24x^94+18x^96+6x^98+10x^100+3x^104+1x^108 The gray image is a code over GF(2) with n=324, k=13 and d=144. This code was found by Heurico 1.16 in 5.68 seconds.