The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+99x^20+16x^21+208x^22+96x^23+511x^24+240x^25+704x^26+320x^27+794x^28+240x^29+432x^30+96x^31+221x^32+16x^33+64x^34+35x^36+3x^40

The gray image is a code over GF(2) with n=108, k=12 and d=40.
This code was found by Heurico 1.16 in 0.342 seconds.