The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  1  X  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  2  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  0  0  0  2

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+147x^16+317x^20+128x^22+1045x^24+4864x^26+1113x^28+128x^30+328x^32+103x^36+15x^40+3x^44

The gray image is a code over GF(2) with n=104, k=13 and d=32.
This code was found by Heurico 1.16 in 1.15 seconds.