The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+61x^16+76x^17+115x^18+96x^19+146x^20+248x^21+190x^22+192x^23+192x^24+240x^25+148x^26+96x^27+110x^28+72x^29+50x^30+2x^32+4x^33+9x^34

The gray image is a code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.16 in 0.11 seconds.