The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+90x^49+228x^50+390x^51+591x^52+860x^53+1080x^54+1452x^55+1782x^56+2160x^57+2687x^58+2992x^59+3481x^60+3886x^61+4118x^62+4398x^63+4520x^64+4432x^65+4357x^66+4090x^67+3762x^68+3272x^69+2762x^70+2256x^71+1669x^72+1328x^73+934x^74+676x^75+473x^76+310x^77+186x^78+118x^79+83x^80+38x^81+25x^82+12x^83+21x^84+8x^85+6x^86+1x^88+1x^90

The gray image is a code over GF(2) with n=128, k=16 and d=49.
This code was found by Heurico 1.10 in 411 seconds.