The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0 X^3  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3
 0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  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+31x^16+32x^18+384x^19+47x^20+16x^24+1x^36

The gray image is a linear code over GF(2) with n=152, k=9 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.