The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1 X+2  1  1 X+2  1  1  2  X  1  1  X  X  1 X+2  X  0
 0  1  1  0 X+1  1 X+3  0  1  3  1  X X+1  1  X  1  1 X+2  3  1  X X+2  3  X  1 X+3  1  1  1
 0  0  X  0  0  0  0  X  X X+2 X+2  X X+2  X  0  2  0  X  2  2  X  2  0  2  0  0  2  X  X
 0  0  0  X  0 X+2 X+2  X  X  X  2  0 X+2 X+2 X+2  X  2 X+2  2 X+2  0  2  2 X+2  2 X+2  2  0  X
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  0  2  0  2  0  2  0  0  2  2  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  0  2
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  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 21.

Homogenous weight enumerator: w(x)=1x^0+52x^21+143x^22+216x^23+501x^24+714x^25+1237x^26+1814x^27+2190x^28+2554x^29+2249x^30+1886x^31+1283x^32+734x^33+440x^34+162x^35+114x^36+42x^37+23x^38+18x^39+7x^40+3x^42+1x^46

The gray image is a code over GF(2) with n=116, k=14 and d=42.
This code was found by Heurico 1.16 in 28.3 seconds.