The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2  1  0  1 X+2  X  1  1  1  0  1  1  2  X  1 X+2  1  1  1
 0  1  0  1  X X+3  1  0 X+3  1  X  2  1 X+1  1  1 X+3  3  X  X X+1  X  1  2  0  1  0 X+1  X
 0  0  1  1  1  0 X+3  X  X  1  1  1  X X+1  X X+1 X+1  X X+3  1  3  1  X  1  2  0  X  1  1
 0  0  0  X  0 X+2 X+2  X  2  2 X+2  0 X+2  0 X+2  X X+2 X+2 X+2 X+2  0  X  2 X+2  0 X+2  0 X+2  2
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  2  0  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  0  0  2  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  2  2  0  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+77x^22+222x^23+530x^24+806x^25+1230x^26+1778x^27+2215x^28+2586x^29+2334x^30+1778x^31+1289x^32+810x^33+376x^34+190x^35+120x^36+22x^37+13x^38+4x^40+2x^42+1x^44

The gray image is a code over GF(2) with n=116, k=14 and d=44.
This code was found by Heurico 1.16 in 3.89 seconds.