The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^64+126x^65+224x^66+316x^67+374x^68+518x^69+591x^70+664x^71+708x^72+732x^73+781x^74+822x^75+924x^76+892x^77+947x^78+946x^79+921x^80+896x^81+799x^82+784x^83+728x^84+600x^85+539x^86+420x^87+314x^88+260x^89+179x^90+126x^91+76x^92+68x^93+26x^94+18x^95+12x^96+2x^97+9x^98+2x^100+2x^101+1x^110

The gray image is a code over GF(2) with n=156, k=14 and d=64.
This code was found by Heurico 1.10 in 17.4 seconds.