The generator matrix

 1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  1  1  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^3+X^2+X X^3  X X^3+X X^2+X X^2+X  X  X X^3+X X^3+X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^3 X^2 X^2 X^2  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3
 0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+210x^16+528x^18+512x^19+664x^20+80x^22+52x^24+1x^32

The gray image is a linear code over GF(2) with n=152, k=11 and d=64.
This code was found by Heurico 1.16 in 1.88 seconds.