The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  2  1  1  1  1  1  X  1
 0  2  0  0  0  0  0  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2
 0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  0  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  2  2  2  2  2  2
 0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  2  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+29x^20+36x^22+95x^24+362x^26+338x^28+98x^30+39x^32+14x^34+7x^36+2x^38+1x^40+2x^44

The gray image is a code over GF(2) with n=108, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0344 seconds.