The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  2  1  0  1  1  1  1 X+2  1  X  1  1  1  1
 0  1  1 X+2 X+3  1  0 X+1  1  3  1  X  2  1 X+1  1  0 X+3 X+2 X+3  1  1  1 X+3  2 X+1 X+3
 0  0  X  0 X+2  0 X+2  0  X  2  X  X  X X+2  0  0  2  X  2 X+2  0 X+2 X+2 X+2 X+2 X+2  X
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  2  2  0
 0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  0  2  2  0
 0  0  0  0  0  2  0  2  0  2  0  0  0  0  2  0  2  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  0  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+68x^21+111x^22+128x^23+325x^24+512x^25+596x^26+640x^27+596x^28+504x^29+306x^30+128x^31+97x^32+64x^33+4x^34+4x^36+4x^37+7x^38+1x^40

The gray image is a code over GF(2) with n=108, k=12 and d=42.
This code was found by Heurico 1.16 in 60.3 seconds.