The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X X+2 X X 1 1 2 1 1 0 2 1 1 1 0 1 X 2 2 1 1 2 X 2 X 1 X X+2 1 1 1 1 1 0 1 1 1 1 X+2 1 1 X 1 1 X+2 1 X 2 X+2 1 X 1 1 1 1 X 2 1 1 1 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 1 1 X 1 1 X+2 1 0 X+3 1 1 0 X X+1 1 2 2 1 1 X+1 X+1 1 0 X 1 3 X 1 3 2 2 X+3 0 1 X+3 X+2 3 X+3 1 X+2 X+2 1 X+3 1 1 X+2 2 1 1 X+1 1 X 1 X+2 2 1 1 3 1 0 0 0 1 1 X+3 X+2 1 X+3 X+2 1 1 0 X X+1 1 2 X 0 X+3 X+3 1 2 1 3 X+2 X+1 X+3 2 1 1 X+2 2 X+3 X+1 1 1 X+3 3 1 0 2 X+2 X+3 X 2 X+2 X+1 3 X+1 X+1 0 X+1 X+3 X+3 X+2 X+2 3 X+2 1 X+2 X+1 X+1 X 1 X+3 X X+1 2 2 0 X 0 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 0 0 0 0 2 0 0 2 2 0 2 2 2 2 0 0 0 2 2 2 0 0 0 2 0 0 0 0 2 0 2 0 0 0 2 0 0 0 2 2 2 2 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 0 0 0 2 0 0 0 2 2 0 2 2 0 0 0 2 2 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 2 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 2 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 0 2 0 2 0 2 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 0 2 2 2 0 2 0 0 2 2 0 2 2 generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+36x^62+114x^63+336x^64+408x^65+639x^66+950x^67+1111x^68+1266x^69+1243x^70+1458x^71+1552x^72+1424x^73+1230x^74+1144x^75+1055x^76+836x^77+592x^78+370x^79+256x^80+136x^81+89x^82+50x^83+31x^84+26x^85+9x^86+10x^87+6x^88+2x^90+3x^92+1x^96 The gray image is a code over GF(2) with n=288, k=14 and d=124. This code was found by Heurico 1.16 in 13.9 seconds.