The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+76x^16+16x^17+144x^18+136x^19+120x^20+240x^21+352x^22+800x^23+1734x^24+256x^25+3744x^26+1200x^27+3648x^28+256x^29+1680x^30+800x^31+491x^32+240x^33+192x^34+136x^35+40x^36+16x^37+16x^38+34x^40+16x^42

The gray image is a code over GF(2) with n=108, k=14 and d=32.
This code was found by Heurico 1.16 in 2.48 seconds.