The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  X  1  1  0  1 X+2  X  1  0  2  1  2  1  1 X+2  1  1
 0  1  0  0  0  1  1  1  1 X+2  X X+2 X+3  3  1  0  1  2  3  0  1 X+1  1  X  3 X+2 X+3  0
 0  0  1  0  1  1  0  3 X+1  2  3  1 X+1  0 X+2  X  1  1  2  X X+3  X  0 X+2  X  1 X+3  1
 0  0  0  1  1  0  1  1  2 X+1 X+2  3  1  0  3 X+3  X  1 X+1  1 X+3  2 X+1  X  1 X+1  2  2
 0  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  2  0  0  2  0  2  0  2  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  0  2  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+179x^22+570x^23+788x^24+1634x^25+1537x^26+2328x^27+2080x^28+2616x^29+1705x^30+1530x^31+701x^32+466x^33+159x^34+52x^35+12x^36+20x^37+4x^38+2x^40

The gray image is a code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.16 in 3.65 seconds.