The generator matrix

 1  0  0  0  0  1  1  1  1  2  1  2 X+2 X+2  1 X+2  X  1  1  1  1  1  1  1  1  2  2  1  1
 0  1  0  0  0  2  1  3 X+3  1  2  1  X X+2 X+1  1  1 X+2  2 X+3  1 X+1  X  3  0  0 X+2 X+2  0
 0  0  1  0  0 X+3 X+1 X+2  X X+3  X  3  1  1  1 X+1  3  3 X+1 X+3  3  2  0  0  3  1  X  1  0
 0  0  0  1  0  1  X  3  X  3 X+3 X+2 X+3  1  3  1  2  0 X+2 X+3  1  X  3  X X+1  X  1 X+3 X+2
 0  0  0  0  1  1  2  2  3 X+1 X+1  3 X+3 X+2 X+1  X  0  3 X+2  2  X X+2  X  3  X X+3 X+3 X+1 X+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+78x^22+514x^23+1025x^24+1740x^25+2701x^26+3308x^27+4630x^28+4630x^29+4644x^30+3532x^31+2870x^32+1696x^33+765x^34+404x^35+144x^36+46x^37+36x^38+2x^39+2x^40

The gray image is a code over GF(2) with n=116, k=15 and d=44.
This code was found by Heurico 1.13 in 5.4 seconds.