The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+34x^24+102x^25+210x^26+156x^27+135x^28+110x^29+116x^30+38x^31+67x^32+28x^33+10x^34+14x^35+3x^36

The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.11 in 0.0122 seconds.