The generator matrix

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

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+200x^21+488x^22+840x^23+1284x^24+1864x^25+2356x^26+2388x^27+2274x^28+1864x^29+1339x^30+832x^31+399x^32+200x^33+40x^34+4x^35+10x^36+1x^46

The gray image is a code over GF(2) with n=108, k=14 and d=42.
This code was found by Heurico 1.16 in 3.52 seconds.