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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+56x^33+140x^34+236x^35+329x^36+422x^37+571x^38+1152x^39+2053x^40+3282x^41+5085x^42+6018x^43+5119x^44+3410x^45+2100x^46+1122x^47+562x^48+442x^49+252x^50+154x^51+117x^52+64x^53+41x^54+22x^55+7x^56+4x^57+3x^58+3x^60+1x^64

The gray image is a code over GF(2) with n=344, k=15 and d=132.
This code was found by Heurico 1.16 in 15.5 seconds.