The generator matrix 1 0 0 0 0 0 0 1 1 1 2 1 1 0 1 1 0 0 1 1 2 2 1 1 0 1 0 2 1 1 1 1 2 2 1 0 0 1 1 1 0 0 1 1 1 2 0 1 1 1 2 2 1 1 2 0 1 0 2 1 1 0 1 2 2 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 0 0 0 1 1 1 1 1 1 3 3 1 1 1 3 3 3 1 2 3 3 1 1 1 1 1 0 1 1 3 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 2 2 0 1 3 1 1 1 3 1 1 3 3 1 0 1 2 3 2 3 3 1 0 2 2 1 2 2 1 1 1 1 0 1 0 0 1 1 0 3 0 2 1 0 2 0 1 1 2 0 1 3 0 1 2 1 3 0 0 0 1 0 0 0 0 0 0 0 3 1 1 3 1 0 1 2 2 1 1 2 1 0 3 3 1 2 1 0 3 2 1 0 2 2 3 0 1 3 0 3 3 1 3 2 1 0 3 2 2 2 3 3 1 2 3 0 1 0 2 0 1 1 3 2 3 0 0 0 0 1 0 0 2 1 3 1 1 1 2 0 0 0 3 3 3 0 1 2 3 3 2 2 3 2 2 1 1 3 3 2 1 2 1 0 1 3 1 2 0 2 2 1 3 2 2 3 1 3 2 2 1 1 2 3 2 3 1 1 2 0 3 0 2 0 0 0 0 0 1 0 3 1 2 3 0 1 1 2 3 3 0 1 2 0 1 2 0 0 2 3 3 1 3 3 1 3 2 0 0 0 2 3 0 2 2 1 0 2 0 3 0 1 3 1 3 1 2 3 2 2 3 0 2 0 2 2 3 2 0 3 3 0 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 0 3 3 3 3 3 1 0 0 0 2 1 2 2 3 2 2 1 1 0 2 1 2 0 2 1 1 0 0 1 1 3 3 3 2 0 0 0 3 1 3 3 1 0 3 0 2 1 2 generates a code of length 68 over Z4 who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+296x^56+718x^58+1113x^60+1444x^62+1718x^64+1808x^66+2056x^68+2056x^70+1685x^72+1482x^74+1042x^76+592x^78+249x^80+88x^82+28x^84+4x^86+2x^88+1x^92+1x^120 The gray image is a code over GF(2) with n=136, k=14 and d=56. This code was found by Heurico 1.16 in 96.7 seconds.