The generator matrix

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

generates a code of length 33 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+58x^20+41x^22+199x^24+32x^25+222x^26+160x^27+555x^28+448x^29+2611x^30+864x^31+6522x^32+9280x^33+6540x^34+864x^35+2661x^36+448x^37+591x^38+160x^39+217x^40+32x^41+174x^42+21x^44+53x^46+5x^48+8x^50+1x^52

The gray image is a code over GF(2) with n=264, k=15 and d=80.
This code was found by Heurico 1.16 in 7.29 seconds.