The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+134x^64+56x^66+470x^68+336x^70+835x^72+712x^74+1174x^76+864x^78+1139x^80+712x^82+780x^84+336x^86+376x^88+56x^90+150x^92+41x^96+18x^100+1x^104+1x^112

The gray image is a code over GF(2) with n=156, k=13 and d=64.
This code was found by Heurico 1.16 in 15.7 seconds.