The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+70x^13+657x^14+2852x^15+9337x^16+27256x^17+53721x^18+73818x^19+54560x^20+27286x^21+9091x^22+2712x^23+614x^24+140x^25+19x^26+10x^27

The gray image is a linear code over GF(2) with n=152, k=18 and d=52.
This code was found by Heurico 1.16 in 94.6 seconds.