The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  2 X+2  1  1  0  1  0 X+2  1  1  1  1  2  2  1  X  1  1
 0  1  0  1  0 X+3  1  X X+2 X+2 X+3  1  1 X+1  3  X  0  1  2  0  X  0  1  1  1 X+3  0  2  X
 0  0  1  1  1  0  1  1  X  1 X+1  1  2  0  3  1 X+3  1  1 X+3  2 X+2  2  0 X+2  2 X+2 X+2  X
 0  0  0  X  0 X+2  2  X  2  X  0 X+2  2  0 X+2  0  0 X+2  X  X X+2  0  2  X X+2  2  2  0 X+2
 0  0  0  0  X  0  2 X+2 X+2  0  X X+2  2  2 X+2  X  2  2  0  X  X  0  X  0  0  0 X+2 X+2  X
 0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  2  0  2  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+80x^22+250x^23+552x^24+802x^25+1245x^26+1848x^27+2178x^28+2394x^29+2306x^30+1848x^31+1255x^32+838x^33+446x^34+176x^35+106x^36+30x^37+18x^38+6x^39+4x^40+1x^42

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 4.19 seconds.