The generator matrix 1 0 1 1 1 X+2 1 1 2 1 1 X 1 2 1 2 1 1 1 X 1 X 1 1 X 1 0 2 1 1 1 1 1 1 X 2 1 2 1 1 2 X 1 1 1 X 1 1 2 X 1 0 1 1 1 X+2 0 X 2 X+2 X+2 2 1 1 0 0 1 1 0 1 2 1 0 1 1 X+2 X+3 1 0 X+1 1 X 3 1 0 1 1 1 2 X+1 X+1 1 X+2 1 0 X+1 1 X 1 1 3 3 3 0 X 0 1 1 3 1 2 0 1 1 3 X+2 1 1 X 2 1 1 X+1 1 X+1 3 0 1 1 X 0 1 1 0 1 0 X 1 3 X+2 X 1 1 0 0 0 X 0 X+2 0 X+2 0 X+2 X+2 2 X 2 X X 0 X+2 2 X+2 X+2 2 0 X+2 0 X X 0 2 0 X+2 X 0 X+2 2 0 X+2 0 X+2 X+2 X+2 X X 2 0 0 X+2 X X+2 2 2 X+2 X 2 2 0 0 0 X+2 X X+2 X+2 X X 0 X+2 X+2 2 X+2 X+2 X X+2 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 2 2 2 0 0 2 0 0 2 2 0 2 2 0 0 2 0 0 2 2 2 2 0 0 0 0 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 2 0 0 0 0 2 0 0 0 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 0 2 0 0 2 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 0 0 0 2 0 0 0 2 2 2 0 2 2 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 0 2 0 0 2 2 0 0 2 2 2 0 0 2 2 2 2 0 2 0 2 0 2 2 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 2 0 0 2 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 2 0 2 2 2 0 2 0 2 2 0 2 2 0 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 0 2 2 0 0 0 0 2 2 0 2 2 2 0 2 2 2 0 2 2 0 2 2 2 2 0 0 0 0 0 0 2 0 2 2 0 2 0 0 0 2 2 0 0 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+24x^62+60x^63+210x^64+160x^65+480x^66+258x^67+782x^68+288x^69+1064x^70+302x^71+1108x^72+276x^73+1052x^74+264x^75+769x^76+204x^77+376x^78+116x^79+168x^80+76x^81+60x^82+22x^83+24x^84+20x^85+4x^86+2x^87+8x^88+8x^90+1x^92+4x^94+1x^96 The gray image is a code over GF(2) with n=288, k=13 and d=124. This code was found by Heurico 1.16 in 4.78 seconds.