The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+212x^16+96x^17+400x^18+576x^19+518x^20+96x^21+112x^22+34x^24+2x^28+1x^32

The gray image is a linear code over GF(2) with n=152, k=11 and d=64.
This code was found by Heurico 1.16 in 0.046 seconds.