The generator matrix

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

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+220x^24+128x^25+416x^26+384x^27+686x^28+512x^29+608x^30+384x^31+441x^32+128x^33+112x^34+58x^36+16x^38+2x^40

The gray image is a code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.16 in 9.2 seconds.