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 2 1 1 0 1 2 1 0 1 2 1 1 1 X+2 X 1 0 1 1 1 0 1 1 1 0 1 X 0 0 1 0 1 1 1 1 1 2 X 1 X+2 2 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 X+1 0 1 2 3 1 X 1 X+1 1 3 X 0 X+1 2 2 X 0 1 3 0 X+2 1 X+1 0 X+3 1 X+2 1 X X+2 0 1 0 X+3 X+3 X+1 3 X 1 0 1 1 X+1 X+1 1 2 2 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+1 X+3 X+2 1 X+3 2 X 3 0 X+2 2 1 X+2 1 X+1 1 1 2 1 2 1 X+2 X+1 X+1 1 X+2 2 2 0 1 1 2 X+3 X+1 X X+3 X+1 3 1 0 2 1 X+2 1 X+3 X+1 3 X 0 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 0 0 2 0 2 2 0 0 0 0 0 2 0 0 2 0 0 0 2 2 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 0 2 2 0 2 0 0 0 2 0 0 2 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 0 2 2 2 2 0 0 2 2 0 2 0 0 0 2 2 2 0 2 2 0 2 0 0 2 2 0 0 2 0 0 2 0 0 2 0 2 2 0 0 0 2 2 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 0 0 2 2 2 2 0 0 0 2 0 0 2 0 2 2 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 0 2 0 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 2 2 0 0 2 2 0 2 2 2 0 2 2 0 2 2 2 0 0 2 2 0 0 0 0 2 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 0 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+61x^58+92x^59+341x^60+388x^61+755x^62+812x^63+1029x^64+1176x^65+1209x^66+1560x^67+1525x^68+1648x^69+1312x^70+1320x^71+832x^72+776x^73+612x^74+300x^75+315x^76+108x^77+112x^78+12x^79+42x^80+29x^82+11x^84+4x^86+1x^90+1x^94 The gray image is a code over GF(2) with n=272, k=14 and d=116. This code was found by Heurico 1.16 in 13.1 seconds.