The generator matrix

 1  0  0  0  0  1  1  1 X+2  1  1  1  X  1  1  1  1  0  1  1  X  1 X+2  0 X+2  1 X+2  1  0
 0  1  0  0  0  0  2  0  2  0  3 X+3  1 X+2  3 X+3 X+3  2  1 X+2  1  X  1  1  1  X  1 X+3  2
 0  0  1  0  0  0  0  2  2  1  1  0  1 X+1 X+1 X+2  X  1 X+3  1 X+2 X+3 X+2  0  3 X+1 X+3  2  1
 0  0  0  1  0  1  X X+1  1  1  2  0  0  X  3  X X+3 X+3 X+3  X X+3  1  3  X  X  0 X+1  1  X
 0  0  0  0  1  1 X+1  X X+1  2 X+2 X+1 X+1 X+1  2 X+2 X+3  0  1  0 X+1  3 X+2  1  3  X X+1  2 X+2
 0  0  0  0  0  2  0  0  2  0  0  2  2  2  0  0  2  2  0  2  0  2  2  0  0  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+446x^22+740x^23+2284x^24+2992x^25+5560x^26+6108x^27+9956x^28+8668x^29+10384x^30+6808x^31+5731x^32+2664x^33+2032x^34+604x^35+388x^36+76x^37+74x^38+12x^39+8x^40

The gray image is a code over GF(2) with n=116, k=16 and d=44.
This code was found by Heurico 1.13 in 31.5 seconds.