The generator matrix

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

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+440x^15+1391x^16+3544x^17+6778x^18+8384x^19+6920x^20+3616x^21+1220x^22+392x^23+68x^24+8x^25+2x^26+4x^28

The gray image is a linear code over GF(2) with n=152, k=15 and d=60.
This code was found by Heurico 1.16 in 7.52 seconds.