The generator matrix

 1  0  0  1  1  1 X^2  1  1  1  1 X^2+X  1  1 X^3+X^2  1  1  1  1
 0  1  0  0 X^3+X^2+1  1  1 X^3  X X^3+1 X^2+X+1  1 X^2+X X^3+X^2  1 X^2+X+1 X^3+1 X+1 X^3+X^2+1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1 X^3+X^2+X  1 X^2+1 X^2  0 X^3 X^2+X X^3+X^2+X X^3+X^2+1 X^3+X^2+X+1 X^2+X X^3+X
 0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  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+298x^16+1264x^17+1312x^18+2532x^19+1303x^20+1132x^21+256x^22+60x^23+29x^24+4x^25+1x^28

The gray image is a linear code over GF(2) with n=152, k=13 and d=64.
This code was found by Heurico 1.16 in 1.19 seconds.