The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+354x^24+424x^25+946x^26+728x^27+1243x^28+784x^29+1342x^30+752x^31+902x^32+328x^33+262x^34+56x^35+57x^36+10x^38+3x^40

The gray image is a code over GF(2) with n=116, k=13 and d=48.
This code was found by Heurico 1.16 in 99 seconds.