The generator matrix

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

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+99x^24+48x^25+212x^26+80x^27+177x^28+80x^29+178x^30+48x^31+78x^32+8x^34+11x^36+2x^38+2x^40

The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.0265 seconds.