The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  4  2  1  4  2  2  2
 0 12  0  0  0  4 12  4  8 12  8  0  0  4  4  4  4  0  4 12  0  8 12 12  4 12  8  4  0
 0  0 12  0  4  4  4  8  0  4  8  4 12  4  8  0  0  4 12  8 12  4  4 12  0  0 12 12  0
 0  0  0 12  4  0  4  4  8  0 12  4  8  4  0  4  4 12  8  0  4 12 12 12 12  0  4  0  8
 0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  8  0  0  8  0  0  0  8  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  0  8  8  0  8  8  8

generates a code of length 29 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+215x^24+72x^25+90x^26+360x^27+786x^28+1168x^29+594x^30+400x^31+211x^32+40x^33+78x^34+8x^35+62x^36+6x^38+5x^40

The gray image is a code over GF(2) with n=232, k=12 and d=96.
This code was found by Heurico 1.16 in 31.2 seconds.