The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+72x^23+226x^24+348x^25+527x^26+884x^27+1118x^28+1458x^29+1891x^30+2268x^31+2856x^32+3090x^33+3107x^34+3094x^35+2811x^36+2510x^37+2118x^38+1534x^39+1016x^40+698x^41+501x^42+318x^43+148x^44+88x^45+47x^46+22x^47+13x^48+1x^50+3x^52

The gray image is a code over GF(2) with n=68, k=15 and d=23.
This code was found by Heurico 1.10 in 21.1 seconds.