The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+46x^21+136x^22+276x^23+386x^24+638x^25+906x^26+1074x^27+1249x^28+1122x^29+906x^30+642x^31+387x^32+234x^33+94x^34+54x^35+22x^36+8x^37+6x^38+2x^39+2x^40+1x^44

The gray image is a code over GF(2) with n=112, k=13 and d=42.
This code was found by Heurico 1.16 in 1.27 seconds.