The generator matrix

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

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+58x^15+121x^16+124x^17+392x^18+670x^19+424x^20+120x^21+48x^22+38x^23+30x^24+12x^25+8x^26+2x^27

The gray image is a linear code over GF(2) with n=152, k=11 and d=60.
This code was found by Heurico 1.16 in 30.5 seconds.