The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X
 0 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3
 0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3
 0  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0
 0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+52x^14+110x^16+96x^18+1536x^19+96x^20+104x^22+48x^24+4x^30+1x^32

The gray image is a linear code over GF(2) with n=152, k=11 and d=56.
This code was found by Heurico 1.16 in 0.031 seconds.