The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  2  2
 0  X  0  0  0  0  0  0  2  2  X X+2 X+2  X X+2 X+2  2  0 X+2  X  X  2 X+2  0  2  0  2  X  2
 0  0  X  0  0  0  0  0  0  0  0  0  0  2  X  X X+2 X+2  X  X  2 X+2 X+2  2 X+2  2  2  X  X
 0  0  0  X  0  0  2 X+2  X  X  X  X X+2  2  0  X  X  2 X+2 X+2  X  X  0  0  2  X  X X+2  2
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2 X+2  0  2  X X+2  X X+2  0  0  2  2  X  0  0  X  2 X+2
 0  0  0  0  0  X  X  2 X+2  X X+2  2  0  X  X  X  0  X  2  X X+2  0  X  2 X+2  X  X  X  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+216x^22+495x^24+634x^26+384x^27+1696x^28+1280x^29+1746x^30+384x^31+723x^32+430x^34+151x^36+46x^38+5x^40+1x^52

The gray image is a code over GF(2) with n=116, k=13 and d=44.
This code was found by Heurico 1.16 in 3.17 seconds.