The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+237x^14+1082x^16+2503x^18+5085x^20+7474x^22+7421x^24+5166x^26+2562x^28+977x^30+231x^32+27x^34+1x^36+1x^40

The gray image is a code over GF(2) with n=46, k=15 and d=14.
This code was found by Heurico 1.16 in 25.3 seconds.