The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+54x^56+38x^58+140x^60+4x^61+123x^62+30x^63+185x^64+96x^65+130x^66+190x^67+170x^68+296x^69+1154x^70+396x^71+10376x^72+416x^73+1198x^74+316x^75+136x^76+180x^77+158x^78+86x^79+106x^80+32x^81+129x^82+6x^83+58x^84+90x^86+30x^88+40x^90+8x^92+11x^94+1x^114

The gray image is a code over GF(2) with n=576, k=14 and d=224.
This code was found by Heurico 1.16 in 10.1 seconds.