The generator matrix

 1  0  0  1  1  1 X^3+X X^3+X^2+X X^3  1  1  1  0 X^2 X^2+X  1  1  1  1
 0  1  0 X^2 X^2+1  1  1  1 X^3+X^2+X X^3+X^2 X^2+1 X^2  1  X X^2+X X^2+X+1 X^3+X^2+X X^3+X  0
 0  0  1 X^2+X+1 X+1 X^2 X^2+1 X^3+X+1  1 X^2+X X^2+1  1 X^2+X  1  1 X^3+X^2+X+1 X^3+X+1 X^3 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+149x^16+492x^17+842x^18+1280x^19+719x^20+382x^21+149x^22+52x^23+27x^24+2x^25+1x^26

The gray image is a linear code over GF(2) with n=152, k=12 and d=64.
This code was found by Heurico 1.16 in 0.125 seconds.