The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  0  0
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  0

generates a code of length 24 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+97x^16+126x^20+128x^22+301x^24+128x^26+180x^28+46x^32+14x^36+3x^40

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0428 seconds.