The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+37x^48+114x^49+279x^50+432x^51+598x^52+886x^53+1127x^54+1378x^55+1742x^56+2284x^57+2590x^58+2922x^59+3453x^60+3784x^61+4156x^62+4504x^63+4530x^64+4382x^65+4319x^66+4052x^67+3653x^68+3244x^69+2724x^70+2170x^71+1668x^72+1308x^73+1073x^74+742x^75+471x^76+340x^77+212x^78+152x^79+90x^80+40x^81+26x^82+28x^83+9x^84+2x^85+5x^86+4x^87+4x^88+1x^90

The gray image is a code over GF(2) with n=128, k=16 and d=48.
This code was found by Heurico 1.10 in 412 seconds.