The generator matrix 1 0 1 1 1 X+2 1 1 0 1 X 1 2 1 1 1 1 0 1 1 X+2 1 1 X+2 X 1 1 1 1 2 1 1 1 1 X 1 1 1 0 1 1 1 0 X+2 X 1 1 X 1 1 1 X+2 X+2 1 1 2 0 X+2 1 1 1 1 0 1 X+2 1 X 1 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 1 0 X+3 2 X+3 1 X 1 1 X 3 1 1 X+3 3 X+2 0 1 X 3 1 2 1 X+1 X+2 0 1 X+3 0 X+1 1 1 1 X+3 X 1 X 1 X 1 1 2 3 1 1 1 3 2 3 X+3 1 X+3 1 X 2 X+1 0 0 X 0 X+2 0 X+2 0 X+2 X+2 X 2 X 2 X X 2 2 X X 0 2 2 0 X X X+2 2 0 X X+2 2 X+2 X+2 X+2 2 0 2 2 2 X 2 X 0 2 X X X+2 X 2 X+2 2 X+2 X 0 2 X X 0 X 2 X+2 X+2 X+2 X X X 2 0 0 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 2 2 2 2 0 0 2 2 2 2 0 2 0 2 2 2 0 2 2 2 0 0 0 0 2 0 0 2 0 0 2 0 2 2 2 0 2 0 0 0 0 2 0 0 0 0 2 2 0 2 0 0 0 2 2 2 2 2 0 2 0 0 2 0 0 0 2 2 0 0 0 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 0 2 2 0 2 0 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 2 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 2 2 0 0 0 2 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 0 2 2 2 2 2 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 2 2 2 2 2 0 0 2 2 2 2 0 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 2 2 2 2 2 2 2 2 0 2 2 0 0 2 0 0 0 0 0 2 0 2 2 0 0 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 0 0 0 2 2 0 2 0 2 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+40x^57+89x^58+158x^59+211x^60+420x^61+585x^62+760x^63+999x^64+1148x^65+1377x^66+1560x^67+1696x^68+1568x^69+1455x^70+1212x^71+943x^72+772x^73+503x^74+346x^75+209x^76+136x^77+67x^78+44x^79+18x^80+8x^81+15x^82+16x^83+10x^84+4x^85+5x^86+7x^88+2x^92 The gray image is a code over GF(2) with n=272, k=14 and d=114. This code was found by Heurico 1.16 in 96.5 seconds.