The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+212x^19+798x^20+1608x^21+3199x^22+4818x^23+7565x^24+9034x^25+10532x^26+9482x^27+7890x^28+4982x^29+3060x^30+1366x^31+637x^32+214x^33+104x^34+26x^35+4x^36+2x^37+1x^38+1x^40

The gray image is a code over GF(2) with n=104, k=16 and d=38.
This code was found by Heurico 1.13 in 16.8 seconds.