The generator matrix

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

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+46x^18+178x^20+420x^22+1240x^24+2188x^26+2212x^28+1304x^30+419x^32+118x^34+42x^36+20x^38+4x^40

The gray image is a code over GF(2) with n=108, k=13 and d=36.
This code was found by Heurico 1.16 in 1.22 seconds.