The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  X  0  1  1  1  0  0  1  1  1
 0  1  0  0  0  0  0  X X+1  X  1 X+1  X  0  X  1  1  1  1 X+1  1  X  1  0  X  X  0
 0  0  1  0  0  0  0  0  1 X+1  X X+1  1 X+1  X  1 X+1  X  0  1  0  0  0  1  0  1  0
 0  0  0  1  0  0  0  0  0  0  0  0  X X+1  1  1  1 X+1  X X+1 X+1  X  X  X  1  X  0
 0  0  0  0  1  0  0  1  0 X+1  X  0  1  X  0  1  1  1  1  1  1  1  X  1  X X+1  0
 0  0  0  0  0  1  0  1  X  X  1 X+1  1 X+1  1 X+1  1 X+1  X  0  0  0 X+1  0 X+1  1  X
 0  0  0  0  0  0  1  1 X+1  0  1  X X+1 X+1  X X+1  0  0 X+1  X  1 X+1  X X+1 X+1  X  X

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+18x^17+103x^18+200x^19+372x^20+496x^21+711x^22+930x^23+1199x^24+1542x^25+1661x^26+1774x^27+1734x^28+1570x^29+1296x^30+1026x^31+695x^32+432x^33+299x^34+162x^35+86x^36+38x^37+25x^38+4x^39+9x^40+1x^42

The gray image is a linear code over GF(2) with n=54, k=14 and d=17.
This code was found by Heurico 1.16 in 8.91 seconds.