The generator matrix

 1  0  0  1  1  1  0  2  0  1  1  1  2  1  1  1 X+2  1  1  1  X X+2  1  X  X  2
 0  1  0  1  X X+3  1  1  1 X+1  1  2  0  0 X+3 X+3  X  0  3 X+2  1  1  2  2 X+2  1
 0  0  1  1  1  0 X+3 X+2 X+1 X+1 X+2  0  1  1  X X+1  1 X+3 X+1  X  2  1  3  1  1  0
 0  0  0  X  0 X+2 X+2  X  0  2  0  X  X  X  0 X+2  2  X X+2  X  X  X  2 X+2  X  X
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  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+285x^20+256x^21+996x^22+976x^23+2318x^24+1808x^25+3028x^26+1888x^27+2386x^28+992x^29+940x^30+208x^31+247x^32+16x^33+28x^34+9x^36+2x^40

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 4.3 seconds.