The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^23+199x^24+374x^25+561x^26+808x^27+1115x^28+1466x^29+1979x^30+2334x^31+2722x^32+3014x^33+3075x^34+3168x^35+2938x^36+2516x^37+2042x^38+1484x^39+1053x^40+722x^41+483x^42+296x^43+147x^44+98x^45+51x^46+22x^47+17x^48+2x^49+1x^50

The gray image is a code over GF(2) with n=68, k=15 and d=23.
This code was found by Heurico 1.16 in 46.7 seconds.