The generator matrix

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

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+28x^22+36x^23+64x^24+120x^25+82x^26+348x^27+92x^28+528x^29+88x^30+348x^31+71x^32+120x^33+44x^34+36x^35+20x^36+12x^38+8x^40+2x^42

The gray image is a code over GF(2) with n=116, k=11 and d=44.
This code was found by Heurico 1.16 in 0.119 seconds.