The generator matrix

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

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+11x^14+42x^15+41x^16+166x^17+526x^18+492x^19+524x^20+148x^21+36x^22+42x^23+6x^24+6x^25+2x^26+4x^28+1x^30

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 0.015 seconds.