The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1 X^3 X^3  1  1 X^2 X^3+X  1  X  1
 0  1  1 X^2 X+1  1  0 X^3+X^2+X+1  1 X^3+X  1  1 X^2+X  0  X  1 X^3+X^2+X+1  X X^3
 0  0  X X^3+X X^3 X^3+X X^3+X^2 X^3+X^2+X X^3+X^2  0 X^2 X^3+X X^2+X X^3+X^2+X X^3+X X^2+X X^3+X X^3+X^2 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+55x^16+340x^17+337x^18+624x^19+376x^20+200x^21+54x^22+48x^23+8x^24+4x^25+1x^26

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 -6.48e-008 seconds.