The generator matrix

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

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+67x^20+190x^21+491x^22+692x^23+835x^24+1178x^25+1255x^26+1184x^27+985x^28+658x^29+353x^30+164x^31+96x^32+22x^33+13x^34+8x^35

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.97 seconds.