The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1 X+2  0  2 X+2  1  1  1  0  1  X  X  1  1  2  1  2  1
 0  1  0  0  0  2  1  3  1  2 X+1  3  1  X  1  1  2  X  3  1  X  2  0  3  1  1 X+2  1  3
 0  0  1  0  0  1  3  2  1 X+1  1 X+2  1  1  2  X X+2 X+3  0 X+1  0  2  1  1 X+3 X+1  X  3  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  3  1  2  0  3  2  3 X+2  3
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  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+542x^24+1380x^26+2260x^28+2056x^30+1447x^32+404x^34+100x^36+2x^40

The gray image is a code over GF(2) with n=116, k=13 and d=48.
This code was found by Heurico 1.13 in 61.3 seconds.