The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  2  1  1  1  1  0  0  1  1  X  0  1  X  1  2  1
 0  1  1  0  1  1  2 X+1  1 X+2  1 X+1 X+1  1  0  2  3  0  1  1 X+1  X  0  X  3  0  2  1  2
 0  0  X  0  0  0  0  0  0  0  0  X  X  X X+2 X+2  2  X  X  X  2  X  X X+2  2  X  X  X X+2
 0  0  0  X  0  0  0  0  X X+2 X+2  X  2  X  0  2 X+2 X+2  2  0  0 X+2  0  X  2  2 X+2  X  2
 0  0  0  0  X  0  2 X+2  0  2  0  2  0 X+2  X  X X+2  X X+2  X X+2  X  2  0  0  X  0  0  2
 0  0  0  0  0  X X+2 X+2 X+2  X  2  2  X  0  0  X  2 X+2  X  2  X  0 X+2  X  X  X  2  2  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+230x^22+100x^23+725x^24+560x^25+1580x^26+1432x^27+2573x^28+1972x^29+2562x^30+1428x^31+1717x^32+536x^33+608x^34+112x^35+195x^36+4x^37+44x^38+4x^40+1x^48

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 12.6 seconds.