The generator matrix

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

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+16x^16+128x^17+310x^18+136x^19+296x^20+112x^21+8x^22+8x^23+6x^24+2x^26+1x^32

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 3.62e-008 seconds.