The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+179x^68+366x^70+482x^72+430x^74+507x^76+420x^78+418x^80+344x^82+350x^84+254x^86+170x^88+86x^90+59x^92+16x^94+9x^96+4x^98+1x^100

The gray image is a code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.16 in 2.99 seconds.