The generator matrix

 1  1  1  1  1  1  1  1  1  X  1 X^2  1  1  X X^2  1  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2  0 X^3  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  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  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+23x^14+34x^15+62x^16+258x^17+302x^18+700x^19+304x^20+252x^21+48x^22+34x^23+16x^24+2x^25+10x^26+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 0.031 seconds.