The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+75x^52+420x^54+1080x^56+2006x^58+3142x^60+4370x^62+5827x^64+7266x^66+8207x^68+8616x^70+7465x^72+6348x^74+4545x^76+2898x^78+1707x^80+930x^82+394x^84+144x^86+63x^88+26x^90+5x^92+1x^96

The gray image is a code over GF(2) with n=138, k=16 and d=52.
This code was found by Heurico 1.10 in 465 seconds.