The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+163x^20+672x^21+1774x^22+3420x^23+6289x^24+9900x^25+14450x^26+18704x^27+20037x^28+18586x^29+14765x^30+10560x^31+6224x^32+3034x^33+1561x^34+592x^35+244x^36+62x^37+25x^38+4x^39+2x^40+2x^41+1x^42

The gray image is a code over GF(2) with n=112, k=17 and d=40.
This code was found by Heurico 1.13 in 67 seconds.