The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+74x^4+64x^6+719x^8+460x^10+1492x^12+1024x^13+732x^14+3072x^15+943x^16+3072x^17+1304x^18+1024x^19+634x^20+1240x^22+225x^24+284x^26+8x^28+12x^30

The gray image is a code over GF(2) with n=32, k=14 and d=4.
This code was found by Heurico 1.16 in 0.534 seconds.