The generator matrix

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

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+110x^16+128x^18+512x^19+224x^20+48x^24+1x^32

The gray image is a linear code over GF(2) with n=152, k=10 and d=64.
This code was found by Heurico 1.16 in 2.81 seconds.