The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  1 X^3  1 X^2+X  1  1  1  1  1  1  0
 0  1 X+1 X^2+X X^2+1  1 X^2+X+1 X^3+X^2+X X^3+1  1 X^3  1 X+1 X^3+X^2+X+1 X^2  X  0 X^2+X  1
 0  0 X^2  0 X^3 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3 X^2 X^2  0 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 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+63x^16+252x^17+515x^18+400x^19+509x^20+240x^21+58x^22+2x^24+4x^25+3x^26+1x^28

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 0.016 seconds.