The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 0 1 1 X+2 1 1 2 1 X 1 1 1 1 1 0 2 1 0 1 1 1 2 X 1 1 1 1 1 1 X+2 2 X 1 1 1 1 X+2 0 X 1 1 2 2 1 2 1 2 2 1 1 0 1 1 0 X+3 1 X X+1 1 3 1 X+2 X+3 0 1 X+2 1 1 2 3 1 X+2 1 3 X+1 X+2 X+3 X 1 1 0 1 X+2 X+1 3 1 1 0 X+3 2 X+1 X+2 X+3 1 1 1 X 3 0 X+3 1 1 X 1 2 1 2 X+2 X X+1 0 2 3 X+1 0 0 X 0 X+2 0 0 X 0 X+2 0 0 0 X X+2 X 2 X X 2 X X X+2 2 X+2 X 2 2 X 2 0 X+2 X+2 X X X+2 0 2 0 2 0 X 0 X+2 0 X+2 X 0 0 2 0 2 X 2 X 0 X 2 X+2 0 X X 0 0 0 0 0 X 0 0 X X X X X+2 2 X X X+2 X X+2 X 2 2 0 2 0 2 0 0 0 X+2 X+2 0 2 X X+2 X X 2 0 X+2 2 X X+2 X 0 X+2 2 0 2 X 2 X+2 0 2 X+2 X X+2 X X X+2 2 X+2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 2 2 0 2 0 2 0 0 2 2 2 2 0 0 2 2 2 2 0 2 2 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 0 0 0 2 2 2 0 0 2 2 0 0 0 0 0 2 0 0 2 2 2 0 0 0 2 2 2 0 2 0 2 2 2 2 0 0 0 2 2 2 0 0 2 2 0 0 0 2 2 0 0 0 0 2 2 0 0 2 2 2 0 0 2 0 0 2 0 0 0 0 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 2 0 0 2 0 0 2 2 2 2 2 0 2 0 0 2 2 2 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 0 0 2 2 2 2 0 2 0 2 0 0 2 2 2 2 2 0 2 0 generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+118x^54+48x^55+438x^56+228x^57+801x^58+540x^59+1283x^60+924x^61+1593x^62+1300x^63+1906x^64+1348x^65+1663x^66+972x^67+1084x^68+532x^69+734x^70+204x^71+335x^72+40x^73+189x^74+8x^75+65x^76+19x^78+7x^80+3x^82+1x^88 The gray image is a code over GF(2) with n=256, k=14 and d=108. This code was found by Heurico 1.16 in 14.4 seconds.