The generator matrix

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

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+34x^22+44x^23+103x^24+124x^25+287x^26+216x^27+434x^28+216x^29+290x^30+124x^31+95x^32+44x^33+24x^34+6x^36+4x^38+1x^40+1x^42

The gray image is a code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in 0.0761 seconds.