The generator matrix

 1  0  0  0  1  1  1 X^2+X  1 X^3+X^2+X X^2  1  1  X  1  0  1 X^3+X^2  1
 0  1  0  0  X X^2 X^3+X X^2+X X^2+1  1  1 X^3+X^2+X+1 X^3+1  1 X^3  1 X^2+X+1  1 X^2
 0  0  1  0 X^3 X^2+1 X^3+X^2+1  1 X^2+X+1  X X^3+1 X+1 X^3+X  1 X^3+X+1 X^3+X+1 X^2 X^3+X X^2+X
 0  0  0  1 X^3+1  1 X^3 X^3+X^2+1  X X^3+X+1 X+1 X+1 X^3+X^2+X+1 X^3+X X^2+1 X^3+1  0  1 X^2

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+780x^15+2596x^16+7004x^17+13600x^18+17448x^19+13724x^20+7288x^21+2324x^22+620x^23+133x^24+12x^25+4x^26+2x^28

The gray image is a linear code over GF(2) with n=152, k=16 and d=60.
This code was found by Heurico 1.16 in 309 seconds.