The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  2  1  1  2  2  0  2  0  1  1  1  1  1  2  1  1  0  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  2  1  3  3  1  1  1  1  2  2  0  3  3  3  1  0  1  2  1  1  0
 0  0  1  0  0  0  0  0  0  3  2  1  3  1  3  3  0  1  2  3  1  1  0  0  1  1  2  2  1  3  2  1  2  2
 0  0  0  1  0  0  0  0  3  1  2  2  1  3  3  1  1  0  1  3  0  1  3  0  2  0  3  0  2  3  0  3  3  0
 0  0  0  0  1  0  0  0  1  0  3  3  2  1  3  1  2  0  1  1  1  3  3  1  2  1  1  3  1  0  1  0  0  2
 0  0  0  0  0  1  0  1  0  3  1  2  1  2  3  1  2  2  0  3  0  0  1  2  3  0  0  0  3  0  1  3  0  0
 0  0  0  0  0  0  1  1  3  2  2  1  1  2  2  3  2  1  2  1  2  3  3  3  1  1  2  0  0  3  1  3  0  0
 0  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  0  0  0  2  2  2  0  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+72x^23+215x^24+350x^25+537x^26+888x^27+1151x^28+1400x^29+1881x^30+2362x^31+2768x^32+3106x^33+3161x^34+2998x^35+2874x^36+2514x^37+2067x^38+1554x^39+1001x^40+740x^41+503x^42+298x^43+175x^44+78x^45+35x^46+20x^47+7x^48+4x^49+7x^50+1x^54

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 56.6 seconds.