The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+92x^52+100x^53+312x^54+432x^55+770x^56+892x^57+1257x^58+1498x^59+1865x^60+2256x^61+2560x^62+2838x^63+3339x^64+3810x^65+4018x^66+4272x^67+4144x^68+4458x^69+4055x^70+4230x^71+3588x^72+3168x^73+2747x^74+2258x^75+1851x^76+1292x^77+1028x^78+714x^79+612x^80+346x^81+348x^82+116x^83+102x^84+54x^85+52x^86+26x^87+18x^88+8x^89+6x^90+2x^92+1x^102

The gray image is a code over GF(2) with n=136, k=16 and d=52.
This code was found by Heurico 1.10 in 475 seconds.