The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  X  X  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X^3+X^2 X^3+X  0  0  0
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  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+40x^14+52x^15+105x^16+372x^17+1152x^18+680x^19+1128x^20+392x^21+72x^22+36x^23+46x^24+4x^25+16x^26

The gray image is a linear code over GF(2) with n=152, k=12 and d=56.
This code was found by Heurico 1.16 in 0.046 seconds.