The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X X^2  1  1 X^2  1  1  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0
 0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 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 X^3 X^3  0 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 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+48x^14+87x^16+256x^17+123x^18+1024x^19+129x^20+256x^21+75x^22+35x^24+9x^26+3x^28+1x^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 0.187 seconds.