The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1  X
 0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  0  2  0  2  2  2  2  2  0
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  0  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  2  2  2  2  0  0  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  0  0  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+98x^20+16x^22+213x^24+160x^26+1024x^27+281x^28+80x^30+133x^32+36x^36+5x^40+1x^44

The gray image is a code over GF(2) with n=108, k=11 and d=40.
This code was found by Heurico 1.16 in 0.993 seconds.