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 2 X 0 0 2 2 1 0 X X X 2 X 0 X 1 1 1 1 X X X 1 2 2 0 1 X 1 0 X 0 0 0 0 0 0 0 X X+2 X X X+2 X 2 X 2 X+2 0 2 2 0 X X+2 X 2 X+2 0 X X X 2 X+2 0 0 X+2 2 0 X X+2 X 0 2 0 X+2 X 0 2 X 0 2 X X+2 2 2 2 X+2 X 0 X+2 2 2 2 2 0 X+2 2 0 0 X 0 0 0 X X+2 X 0 0 0 X X X+2 2 X X+2 2 X+2 X 2 2 2 X 0 X+2 0 2 0 2 X X X X X X X 2 X 0 2 2 0 0 X 0 X X X X X+2 2 0 X+2 2 0 X 2 X 0 2 X X X 2 X 0 0 0 0 X 0 X X X+2 0 X X 2 0 2 X+2 X X+2 X+2 X+2 X 0 X 2 0 X 0 2 X+2 2 X+2 2 X+2 X+2 0 X+2 0 X+2 X+2 2 0 2 2 X X X X X+2 X X+2 X+2 X+2 2 X+2 X 0 X 0 0 X X X+2 0 X+2 2 X 0 0 0 0 0 0 0 X X 0 X+2 X 2 X+2 X+2 0 X+2 X 2 0 X 2 0 X X X+2 X+2 X 2 2 X 0 2 2 X X 0 2 X 0 X 2 2 2 2 2 X+2 X 2 X+2 0 X 2 X 2 X+2 X X 0 2 X 0 2 2 0 X+2 0 X+2 X X X 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 2 0 2 0 2 2 2 2 0 2 2 2 0 2 0 0 0 2 2 0 2 0 2 2 2 2 0 2 0 0 0 2 2 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0 0 0 0 0 2 0 2 2 0 2 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 2 2 2 2 2 0 2 0 2 2 2 0 0 2 0 2 2 2 0 2 2 0 2 2 0 0 0 0 0 2 2 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 0 2 0 0 2 2 2 0 2 0 0 2 0 2 0 0 0 0 2 2 2 0 0 2 2 2 0 0 0 0 0 2 2 0 0 2 2 2 0 2 0 2 2 0 2 0 2 2 0 0 2 0 2 0 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+52x^56+82x^57+200x^58+234x^59+387x^60+438x^61+543x^62+736x^63+1017x^64+1166x^65+1178x^66+1450x^67+1475x^68+1480x^69+1278x^70+1178x^71+869x^72+704x^73+579x^74+392x^75+311x^76+184x^77+151x^78+94x^79+106x^80+40x^81+34x^82+12x^83+3x^84+2x^85+2x^86+3x^88+1x^90+2x^94 The gray image is a code over GF(2) with n=272, k=14 and d=112. This code was found by Heurico 1.16 in 21.4 seconds.