The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+121x^20+516x^21+861x^22+1314x^23+1845x^24+2216x^25+2493x^26+2386x^27+1975x^28+1284x^29+751x^30+422x^31+118x^32+48x^33+23x^34+6x^35+4x^36

The gray image is a code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 3.18 seconds.