The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+254x^22+148x^23+671x^24+556x^25+1683x^26+1452x^27+2424x^28+1812x^29+2698x^30+1484x^31+1587x^32+564x^33+700x^34+116x^35+175x^36+12x^37+40x^38+5x^40+1x^42+1x^52

The gray image is a code over GF(2) with n=116, k=14 and d=44.
This code was found by Heurico 1.16 in 6.14 seconds.