The generator matrix

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

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+59x^22+112x^23+216x^24+462x^25+601x^26+804x^27+1185x^28+1298x^29+1190x^30+904x^31+579x^32+402x^33+174x^34+100x^35+62x^36+14x^37+23x^38+4x^40+1x^42+1x^44

The gray image is a code over GF(2) with n=116, k=13 and d=44.
This code was found by Heurico 1.16 in 1.36 seconds.