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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+62x^35+137x^36+178x^37+127x^38+662x^39+292x^40+1312x^41+206x^42+640x^43+158x^44+140x^45+40x^46+40x^47+42x^48+32x^49+10x^50+2x^51+9x^52+2x^53+1x^54+2x^55+1x^64

The gray image is a code over GF(2) with n=328, k=12 and d=140.
This code was found by Heurico 1.16 in 45.6 seconds.