The generator matrix
1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 1 1 1 X
0 X 0 X^2+X X^2 X^3+X^2+X X^3+X^2 X 0 X^3 X^2+X X X^3+X^2 X^3+X^2 X^3+X^2+X X X^2+X X^3+X X^3
0 0 X^3+X^2 0 X^2 X^2 X^3 X^2 0 X^2 0 X^3 X^2 0 X^3+X^2 X^3+X^2 X^2 X^3 X^2
0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 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+54x^16+64x^17+280x^18+256x^19+248x^20+64x^21+40x^22+16x^24+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 0.016 seconds.