The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  2  1  X  1  1  0  1  1  1  X  X X+2  1  2  2  1
 0  1  1  0  1  1  0 X+1  1  2  1 X+1  0  1 X+3  1 X+2  2  1  3  3 X+2  1 X+2  1  0  X  X  2
 0  0  X  0  0  0  0  0  0  2  2  X  X X+2  2 X+2 X+2  X  X  2  X  2  X  0  2  X  X  2  X
 0  0  0  X  0  0 X+2  2 X+2  0  X  X  X  0 X+2 X+2  2  2 X+2 X+2 X+2  X  X  X X+2  X  X X+2  X
 0  0  0  0  X X+2 X+2  2  X  X  0  2  0  2  0  X X+2  2  0  X  X  X  2  X X+2  X X+2  0 X+2
 0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  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+80x^22+124x^23+241x^24+408x^25+671x^26+936x^27+1031x^28+1226x^29+1072x^30+860x^31+694x^32+390x^33+244x^34+128x^35+49x^36+22x^37+12x^38+2x^41+1x^42

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 1.32 seconds.