The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  2  1  X  1  1  1  2  X  0  1  1  1
 0  1  1  0 X+1  1  X X+3  1  3  1 X+2  2 X+1  1 X+3  1  0  1  3 X+2  0  X  X  1  3 X+1  0
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  X  0  0  X  X  2  X  0  2  2  X  X  0  0  0  0
 0  0  0  2  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  0  2  2  2  0  2  0  2  0  0  2  0  2  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+27x^20+62x^21+146x^22+170x^23+496x^24+470x^25+1136x^26+826x^27+1518x^28+834x^29+1140x^30+494x^31+488x^32+162x^33+128x^34+46x^35+23x^36+8x^37+10x^38+6x^40+1x^48

The gray image is a code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 1.07 seconds.