The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+123x^20+16x^21+180x^22+224x^23+844x^24+752x^25+1396x^26+1088x^27+1503x^28+752x^29+700x^30+224x^31+303x^32+16x^33+28x^34+37x^36+4x^40+1x^44

The gray image is a linear code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 2.21 seconds.