The generator matrix

1 0 0 0 0 0 1 1 1 2 1 1 1 1 1 2 1 1 2 1 2 2 1 0 1 0 1 2 0 1 1 1 1 2 2 1 1 1 1 1 2 1 2 0 0 2 1 0 1 1 1 1 1 0 1 1 0 2 2 1 1 1 1 0 1 0 1 1
0 1 0 0 0 0 0 0 0 0 0 1 1 1 3 1 1 2 1 2 0 1 3 1 2 1 3 1 0 3 2 2 3 1 1 2 1 1 1 3 1 2 0 1 1 2 0 1 2 2 2 0 3 1 2 0 1 1 0 3 3 1 1 1 1 2 2 0
0 0 1 0 0 0 0 0 0 0 1 0 2 2 1 1 1 3 3 1 1 2 3 0 3 0 3 3 1 1 0 2 2 1 0 3 0 0 3 1 2 2 1 2 1 1 2 1 0 2 3 1 1 3 3 2 3 2 2 0 3 0 3 1 2 1 0 0
0 0 0 1 0 0 0 1 1 1 2 2 0 1 1 1 3 2 0 3 1 3 0 1 1 2 0 2 1 2 3 2 2 2 0 0 3 2 0 3 2 2 3 2 3 3 2 3 1 1 0 0 1 0 0 2 3 1 1 1 0 1 0 2 3 0 0 1
0 0 0 0 1 0 1 0 1 3 2 2 1 3 2 2 3 1 3 2 0 2 2 3 3 3 3 2 3 0 0 3 3 3 2 2 0 2 1 1 1 2 0 0 1 1 3 3 0 2 1 1 1 1 0 0 2 1 3 2 3 0 0 0 3 0 1 0
0 0 0 0 0 1 1 3 2 1 1 3 0 1 3 0 0 0 0 2 3 3 0 0 3 3 1 1 0 0 1 1 2 0 2 3 2 3 0 0 1 2 3 1 2 2 0 2 0 2 1 3 3 1 2 3 3 0 2 0 1 2 1 1 0 0 2 0
0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 0 0 2 2 2 0 2 0 2 2 0 2 0 0 2 0 2 0 2 0 0 2 0 2 2 0 2 0 2 2 0 0 2 2 2 0 0 2

generates a code of length 68 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+37x^56+100x^57+191x^58+262x^59+305x^60+354x^61+381x^62+400x^63+423x^64+426x^65+485x^66+502x^67+483x^68+538x^69+463x^70+472x^71+455x^72+400x^73+384x^74+298x^75+258x^76+174x^77+108x^78+88x^79+77x^80+50x^81+31x^82+26x^83+6x^84+6x^85+4x^86+3x^88+1x^98

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.10 in 3.86 seconds.