The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+307x^56+706x^58+1080x^60+1450x^62+1757x^64+1858x^66+2034x^68+1976x^70+1747x^72+1448x^74+1010x^76+644x^78+234x^80+108x^82+20x^84+2x^86+1x^88+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 1.10 in 15.2 seconds.