The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0 X+2  1  1  0  1  1  1 X+2  1  X  X  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1  1 X+2  3  1  0 X+2 X+1  1 X+3  0  0 X+1
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  0  2  0  0  2  0  0
 0  0  0  0  0  2  0  0  2  2  0  2  0  0  2  0  2  2  2  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  2  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+30x^20+42x^21+61x^22+298x^23+147x^24+722x^25+294x^26+946x^27+270x^28+734x^29+128x^30+286x^31+43x^32+38x^33+26x^34+6x^35+20x^36+3x^38+1x^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 0.252 seconds.