The generator matrix

 1  0  0  1  1  1  2  2  1  1  2  1  1  2  0  1  1 X+2  1  1 X+2  X  1  2  1  1  1  1  1
 0  1  0  0  1 X+1  1  0  2 X+1  1  0  1  1  1 X+2 X+3  1 X+2 X+3  1 X+2  3  1  1  2  X X+1 X+1
 0  0  1  1  1  0 X+1  1  0  2 X+1 X+1 X+3  X  0  3 X+2 X+2  2 X+1 X+3  1  0  X X+2 X+1 X+3  0  0
 0  0  0  X  0  X  X  0  0  X  X X+2  2  2 X+2  2  2 X+2  X X+2  0 X+2  X X+2  X  X X+2  0  2
 0  0  0  0  X  X  2 X+2 X+2  2 X+2 X+2  2  0  X  2  X  2 X+2  2  2  2  2  X  X  2 X+2  2 X+2

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+102x^23+208x^24+568x^25+547x^26+1162x^27+805x^28+1442x^29+783x^30+1230x^31+512x^32+502x^33+169x^34+94x^35+39x^36+14x^37+5x^38+4x^39+3x^40+2x^41

The gray image is a code over GF(2) with n=116, k=13 and d=46.
This code was found by Heurico 1.16 in 1.16 seconds.