The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  2  X  1  1  1  X  2  2  0  X
 0  X  0  0  0  0  0  2  2  X X+2  X  2 X+2  X  X  0 X+2  0  2 X+2 X+2  X  X  2  X  X  0  0
 0  0  X  0  0  2 X+2  X  X  X  X  X X+2  2  X  2  0  2  X  2  X  2 X+2  0  0  0  0  0  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X X+2 X+2  2  2  2  X  X  0 X+2  X  X  X  2 X+2  2  0
 0  0  0  0  X  X  2 X+2  X X+2  2  2  0  X  X  X  0  0  0  X  X  2  X  X  2 X+2  0  X  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+217x^24+68x^25+88x^26+244x^27+274x^28+392x^29+84x^30+264x^31+203x^32+52x^33+80x^34+4x^35+70x^36+4x^38+3x^40

The gray image is a code over GF(2) with n=116, k=11 and d=48.
This code was found by Heurico 1.16 in 0.121 seconds.