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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+155x^40+12x^41+218x^42+124x^43+475x^44+600x^45+942x^46+696x^47+432x^48+92x^49+172x^50+12x^51+91x^52+38x^54+27x^56+6x^58+2x^60+1x^72

The gray image is a code over GF(2) with n=368, k=12 and d=160.
This code was found by Heurico 1.16 in 13.9 seconds.