The generator matrix

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

generates a code of length 24 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+102x^14+518x^16+1032x^18+1864x^20+3030x^22+3320x^24+2858x^26+2078x^28+1068x^30+375x^32+102x^34+34x^36+2x^40

The gray image is a code over GF(2) with n=48, k=14 and d=14.
This code was found by Heurico 1.10 in 2.44 seconds.