The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  2  1  X  1  1  1  0  1 X+2  2  1  1  2  1
 0  1  1  0  1  1  0 X+1  1  2  1 X+1  0  1 X+3  1 X+2  3 X+1  1  2  1  1 X+3  0  1  0
 0  0  X  0  0  0  0  0  0  2  2  X  X X+2 X+2  X  X  0  2  X  0  X X+2  2  X X+2  0
 0  0  0  X  0  0 X+2  2 X+2  0  X  X  X  0 X+2 X+2  2 X+2  2 X+2 X+2  0 X+2 X+2  2 X+2  0
 0  0  0  0  X X+2 X+2  2  X  X  0  2  0  2  X X+2  X  0  2  2  0  X  X  2  X X+2  0
 0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  2  2  0  0  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+70x^20+104x^21+202x^22+400x^23+479x^24+1256x^25+795x^26+1616x^27+771x^28+1240x^29+480x^30+400x^31+204x^32+88x^33+57x^34+16x^35+11x^36+1x^38+1x^46

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 1.2 seconds.