The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+114x^20+86x^22+527x^24+1048x^26+2354x^28+2132x^30+1353x^32+312x^34+219x^36+6x^38+39x^40+1x^52

The gray image is a code over GF(2) with n=116, k=13 and d=40.
This code was found by Heurico 1.16 in 1.63 seconds.