The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+321x^56+716x^58+1070x^60+1360x^62+1796x^64+1900x^66+2036x^68+1987x^70+1790x^72+1400x^74+1019x^76+578x^78+264x^80+120x^82+18x^84+3x^86+3x^88+1x^92+1x^112

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 88.4 seconds.