The generator matrix

 1  0  0  1  1  1 X+2  1  1  X  1  1  2  0  0  2  1  1  1  1  X  2  0  2 X+2  2 X+2  X
 0  1  0  0  1 X+3  1  X X+1  1  X  3  1 X+2  1  1  X  2 X+1 X+3 X+2  X  2  1  1  1  0  1
 0  0  1 X+1  1 X+2 X+3  X X+3  1  1  0  X  1 X+1  1  3  0  0  1  1  1  1 X+3  1  1  1  X
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  2
 0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  0  0  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+85x^22+306x^23+324x^24+844x^25+684x^26+1356x^27+910x^28+1512x^29+686x^30+852x^31+273x^32+204x^33+76x^34+44x^35+26x^36+5x^38+2x^39+2x^40

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 0.976 seconds.