The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  1  1  X  1  X  2  1  1
 0  X  0  0  0  0  0  2  2  X X+2 X+2 X+2 X+2  2 X+2  X  0 X+2 X+2  2  X  0  0 X+2  X  2  0
 0  0  X  0  0  2 X+2  X  X  X  X X+2  0  X  X  0  0  2  2 X+2  2  X X+2  X X+2 X+2 X+2  2
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2 X+2  X  0 X+2  X  X X+2  X  0 X+2  2  2  0 X+2  2  0  0
 0  0  0  0  X  X  2 X+2  X X+2  2  0  X X+2  X X+2  2 X+2  0 X+2 X+2  0  0  X X+2  0  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+23x^22+78x^23+143x^24+174x^25+243x^26+264x^27+258x^28+288x^29+189x^30+142x^31+95x^32+46x^33+57x^34+28x^35+14x^36+4x^37+1x^40

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 0.104 seconds.