The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+234x^24+128x^25+320x^26+128x^27+200x^28+12x^32+1x^48

The gray image is a code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 0.14 seconds.