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 X 0 1 1 1 1 X 1 X 1 1 1 0 1 1 0 1 1 1 1 1 X 1 1 1 0 1 1 X 1 0 X X 1 1 1 1 1 X 1 1 1 1 X 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 2 X+2 X+2 0 0 X+2 X 2 0 2 2 X+2 X X X X+2 X X+2 X+2 X+2 X+2 0 0 X 0 0 X 0 X+2 0 2 X X+2 0 2 2 X 2 2 X+2 X+2 X 2 X+2 2 X X X+2 X X+2 0 X X+2 2 X+2 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 0 2 0 2 0 2 2 0 2 0 0 2 2 2 0 2 2 2 2 0 2 0 0 0 0 0 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 2 0 2 2 0 2 2 2 0 2 0 2 2 2 0 0 2 0 2 2 2 2 0 2 2 2 0 0 0 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 0 0 2 2 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 2 2 2 2 2 0 0 2 2 0 2 2 2 0 2 0 0 2 2 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 2 0 0 0 2 2 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 2 0 0 2 2 2 0 2 0 0 2 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 0 2 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 0 0 2 2 0 2 0 2 0 0 0 0 2 2 2 0 2 0 0 2 2 2 2 0 0 0 0 2 0 2 0 2 2 0 0 0 2 0 2 0 2 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 2 2 0 0 2 0 0 0 2 0 0 2 2 0 0 0 2 2 2 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 2 2 0 0 2 0 0 2 2 2 2 0 2 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+68x^62+188x^64+223x^66+32x^67+349x^68+160x^69+475x^70+320x^71+512x^72+320x^73+479x^74+160x^75+353x^76+32x^77+200x^78+97x^80+67x^82+22x^84+15x^86+10x^88+5x^90+3x^92+2x^94+2x^98+1x^116 The gray image is a code over GF(2) with n=288, k=12 and d=124. This code was found by Heurico 1.16 in 8.14 seconds.