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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+183x^56+517x^58+705x^60+840x^62+908x^64+980x^66+1001x^68+932x^70+822x^72+588x^74+357x^76+215x^78+106x^80+23x^82+12x^84+1x^86+1x^92

The gray image is a code over GF(2) with n=134, k=13 and d=56.
This code was found by Heurico 1.10 in 3.89 seconds.