The generator matrix

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

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+268x^20+384x^21+964x^22+1140x^23+1912x^24+2004x^25+2864x^26+2192x^27+2072x^28+1096x^29+868x^30+308x^31+223x^32+36x^33+40x^34+8x^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 12.1 seconds.