The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  1  X X^2  1  X X^3
 0  X  0  X X^3  0 X^2+X X^3+X^2 X^2+X X^3+X^2 X^3+X^2 X^3+X X^2 X^3+X^2+X X^2+X X^3+X^2  0 X^3+X X^2
 0  0  X  X X^2 X^2+X X^2+X X^2  0 X^3+X X^3 X^2+X  X  0 X^2+X  X X^2 X^3+X^2+X X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0 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+146x^16+268x^17+402x^18+476x^19+367x^20+236x^21+92x^22+36x^23+13x^24+8x^25+2x^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 0.234 seconds.