The generator matrix

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

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+162x^15+722x^16+1636x^17+3285x^18+4754x^19+3394x^20+1588x^21+626x^22+170x^23+27x^24+8x^25+9x^26+2x^27

The gray image is a linear code over GF(2) with n=152, k=14 and d=60.
This code was found by Heurico 1.16 in 0.672 seconds.