The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+142x^22+184x^23+337x^24+216x^25+387x^26+216x^27+238x^28+104x^29+140x^30+48x^31+28x^32+3x^34+4x^36

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 0.0591 seconds.