The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+148x^23+199x^24+348x^25+190x^26+348x^27+229x^28+264x^29+92x^30+140x^31+48x^32+28x^33+6x^34+4x^35+3x^36

The gray image is a code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.16 in 1.69 seconds.