The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1  1 X+2  1  1  1  0  1  1  X  X  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  3  1 X+2 X+1  0  1 X+2 X+1  3  1  0 X+1  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  2  0  0  2  2  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  2  2  0  2  0  2  0  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  0  2  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+80x^20+102x^22+16x^23+420x^24+224x^25+712x^26+752x^27+1275x^28+1088x^29+1172x^30+752x^31+819x^32+224x^33+296x^34+16x^35+195x^36+22x^38+24x^40+1x^44+1x^52

The gray image is a code over GF(2) with n=116, k=13 and d=40.
This code was found by Heurico 1.16 in 1.07 seconds.