The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^14+206x^15+328x^16+610x^17+959x^18+1380x^19+1889x^20+2478x^21+3083x^22+3480x^23+3601x^24+3528x^25+3258x^26+2516x^27+1890x^28+1440x^29+859x^30+570x^31+341x^32+134x^33+79x^34+40x^35+13x^36+2x^37+1x^38+1x^40

The gray image is a code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.16 in 23 seconds.