The generator matrix

 1  0  0  0  1  1  1  0  1  1  X X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  2  1  1  0  1
 0  1  0  0  0  1  3  1  X X+3  1  2  3  2  1 X+3  2 X+2  3  1  2  X  X  0  2 X+1  X  X  0
 0  0  1  0  1  1  0 X+1 X+1 X+2  1  1  1  0  2  X X+2  1 X+2 X+1  0 X+2 X+1  1  X X+3  3 X+2  0
 0  0  0  1  1  0 X+1 X+1  X  2  0  1  3  1  1  3  2  X  2  X  X X+3 X+3 X+1  1 X+1  2  0  0
 0  0  0  0  2  0  2  0  0  0  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0
 0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  0  2  2  0  2  0  0  2  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+102x^22+296x^23+577x^24+822x^25+1321x^26+1786x^27+2087x^28+2372x^29+2151x^30+1798x^31+1302x^32+856x^33+503x^34+246x^35+121x^36+12x^37+19x^38+2x^39+8x^40+2x^41

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 3.58 seconds.