The generator matrix

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

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+34x^20+82x^22+48x^23+227x^24+240x^25+561x^26+480x^27+784x^28+480x^29+528x^30+240x^31+205x^32+48x^33+102x^34+22x^36+6x^38+7x^40+1x^42

The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.247 seconds.