The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  1  X  X  X  0  1  1  1  1  X
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  0  0 X+2  2 X+2  X X+2  2  0  0  0  0  2
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2  X  X X+2  0  X  0  X X+2  X  0  X  X X+2  X
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  2  2  2  2  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  0  0  0  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  2  0  2  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  0  0  0  2  2  0  2  2  2  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+86x^22+278x^24+64x^25+492x^26+256x^27+682x^28+384x^29+702x^30+256x^31+489x^32+64x^33+234x^34+78x^36+20x^38+8x^40+2x^42

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 0.68 seconds.