The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2 X+2  1  1  1  1  0  0  1  1 X+2  1 X+2  1  0  0
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  3  0 X+2 X+1  1  1 X+1  0  1  3  1 X+1  1  1
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  2  2  0  2  0  2
 0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  2  2  2  0  2  2
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  2  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  2  2  0  0  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+123x^20+16x^21+180x^22+224x^23+844x^24+752x^25+1396x^26+1088x^27+1503x^28+752x^29+700x^30+224x^31+303x^32+16x^33+28x^34+37x^36+4x^40+1x^44

The gray image is a code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 2.26 seconds.