The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+26x^18+28x^19+137x^20+160x^21+392x^22+716x^23+1227x^24+1884x^25+2318x^26+2612x^27+2290x^28+1900x^29+1264x^30+708x^31+401x^32+148x^33+86x^34+32x^35+37x^36+4x^37+8x^38+3x^40+2x^42

The gray image is a code over GF(2) with n=108, k=14 and d=36.
This code was found by Heurico 1.16 in 3.3 seconds.