The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  2  1  1  1  1  0  2  1  1 X+2  1  2  1  1
 0  1  1  0  1  1  2 X+1  1 X+2  1 X+1 X+1  1  0 X+3  X  3  1  1 X+3  0  1 X+2  1 X+1  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X X+2  X  X  2  2  2  X  0 X+2  X  2  X X+2
 0  0  0  X  0  0  0  0  X X+2 X+2  X  2  X  0 X+2  2  X  X  0  X X+2  2 X+2  2  0  2
 0  0  0  0  X  0  2 X+2  0  2  0  2  0 X+2  X  2  X X+2  2  X  X  X  X X+2  0  X  2
 0  0  0  0  0  X X+2 X+2 X+2  X  2  2  X  0  0 X+2 X+2  X X+2  2  0  2  X X+2  2  X  X

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+189x^20+44x^21+598x^22+456x^23+1466x^24+1364x^25+2804x^26+2416x^27+2969x^28+1364x^29+1500x^30+456x^31+517x^32+44x^33+148x^34+41x^36+6x^38+1x^44

The gray image is a code over GF(2) with n=108, k=14 and d=40.
This code was found by Heurico 1.16 in 4.38 seconds.