The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  1  X  1  0  1  1  X  0  X  1  1  1  1  X  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2 X+2  X  2 X+2  0  X  0 X+2 X+2  X X+2  0 X+2 X+2  2 X+2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  2  0  2  2  0  0  0  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  2  2  2  0  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+74x^20+56x^22+274x^24+532x^26+1134x^28+1028x^30+675x^32+156x^34+114x^36+20x^38+26x^40+6x^44

The gray image is a code over GF(2) with n=116, k=12 and d=40.
This code was found by Heurico 1.16 in 0.38 seconds.