The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+46x^20+54x^21+141x^22+278x^23+365x^24+1038x^25+932x^26+2252x^27+1586x^28+2944x^29+1590x^30+2344x^31+939x^32+1024x^33+372x^34+244x^35+118x^36+58x^37+37x^38+2x^39+13x^40+2x^41+2x^44+2x^48

The gray image is a code over GF(2) with n=116, k=14 and d=40.
This code was found by Heurico 1.16 in 3.93 seconds.