The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+6x^17+15x^18+212x^19+15x^20+6x^21+1x^38

The gray image is a linear code over GF(2) with n=152, k=8 and d=68.
This code was found by Heurico 1.16 in 0.016 seconds.