The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  X  2  1  1  1  X  0  1  1
 0  X  0  0  0  0  0  0  0  X X+2  X  2  2  X  0  2 X+2  X  X  0  X X+2 X+2  2  2  0 X+2  2
 0  0  X  0  0  0  X X+2  X  X  X  0  0  X  2  X X+2 X+2  2  0  0  X  2  2  X  2  2  0  0
 0  0  0  X  0  X  X  X  2  0  0  2  2  2 X+2 X+2  0  X X+2 X+2  X  2 X+2 X+2  2  0  0  0  X
 0  0  0  0  X  X  2 X+2 X+2  0  X  X  0 X+2  X  2  X X+2  2 X+2  X  2 X+2 X+2  2 X+2  X  2  0
 0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  2  0  2  2  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 22.

Homogenous weight enumerator: w(x)=1x^0+43x^22+80x^23+150x^24+202x^25+283x^26+428x^27+556x^28+620x^29+560x^30+454x^31+269x^32+194x^33+117x^34+56x^35+48x^36+8x^37+20x^38+6x^39+1x^46

The gray image is a code over GF(2) with n=116, k=12 and d=44.
This code was found by Heurico 1.16 in 0.397 seconds.