The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X+2  0  X X+2  1 X+2  2  1  1  X  1  2  X  1  1  1  1  X
 0  1  0  X  1 X+3  1 X+2  X X+1 X+1  1  1  X  0 X+1  1  1  2  2  1 X+1  X X+2  3  X  3  X  1
 0  0  1  1 X+3 X+2  1 X+3  X X+1  0  0 X+1  1  1  0 X+1  X  1  X X+2  3  1  1  0 X+2  3  1  X
 0  0  0  2  0  0  0  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  0  2  2  2  0  2  0  2  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  0  0  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2  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+135x^22+128x^23+625x^24+608x^25+1546x^26+1312x^27+2809x^28+1984x^29+2830x^30+1472x^31+1561x^32+480x^33+588x^34+160x^35+118x^36+19x^38+5x^40+2x^42+1x^44

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 6.58 seconds.