The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+186x^21+490x^22+812x^23+1470x^24+1716x^25+2342x^26+2252x^27+2488x^28+1744x^29+1472x^30+804x^31+389x^32+124x^33+46x^34+36x^35+4x^36+6x^37+2x^38

The gray image is a code over GF(2) with n=108, k=14 and d=42.
This code was found by Heurico 1.13 in 1.38 seconds.