The generator matrix

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

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+58x^20+76x^21+93x^22+198x^23+299x^24+382x^25+588x^26+752x^27+560x^28+376x^29+291x^30+182x^31+95x^32+62x^33+51x^34+20x^35+10x^36+1x^40+1x^42

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 0.353 seconds.