The generator matrix

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

generates a code of length 30 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+72x^22+94x^23+215x^24+350x^25+506x^26+922x^27+1832x^28+2734x^29+2932x^30+2726x^31+1841x^32+938x^33+528x^34+334x^35+197x^36+74x^37+52x^38+20x^39+7x^40+6x^42+2x^44+1x^52

The gray image is a code over GF(2) with n=240, k=14 and d=88.
This code was found by Heurico 1.16 in 2.46 seconds.