The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+43x^14+308x^16+600x^18+1284x^20+1858x^22+1805x^24+1356x^26+644x^28+235x^30+53x^32+4x^34+1x^40

The gray image is a code over GF(2) with n=46, k=13 and d=14.
This code was found by Heurico 1.16 in 1.42 seconds.