The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+134x^22+108x^23+624x^24+532x^25+1104x^26+848x^27+1420x^28+984x^29+1141x^30+508x^31+513x^32+84x^33+143x^34+8x^35+32x^36+5x^38+2x^40+1x^42

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 1.06 seconds.