The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+11x^26+8x^27+20x^28+176x^29+20x^30+8x^31+11x^32+1x^58

The gray image is a code over GF(2) with n=116, k=8 and d=52.
This code was found by Heurico 1.16 in 0.0101 seconds.