The generator matrix

 1  1  1  1  1  1  1  1  0 X^3+X^2 X^3  1  1  1  1  X  X  0  1
 0  X  0  X X^3 X^3+X  0  X  X  X X^2 X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^2  0 X^3+X^2 X^3
 0  0  X  X X^2 X^2+X X^2+X X^2 X^3 X^2+X  X  X  0 X^2 X^2+X  X X^3+X^2+X  X 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+23x^16+184x^17+185x^18+312x^19+136x^20+104x^21+30x^22+40x^23+8x^24+1x^26

The gray image is a linear code over GF(2) with n=152, k=10 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.