The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^16+42x^17+123x^18+176x^19+161x^20+178x^21+162x^22+256x^23+188x^24+174x^25+188x^26+128x^27+108x^28+54x^29+38x^30+16x^31+2x^32+1x^34+3x^36

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 0.112 seconds.