The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+240x^20+48x^21+644x^22+480x^23+1635x^24+1488x^25+2584x^26+2112x^27+2648x^28+1488x^29+1608x^30+480x^31+673x^32+48x^33+152x^34+48x^36+4x^38+3x^40

The gray image is a code over GF(2) with n=108, k=14 and d=40.
This code was found by Heurico 1.16 in 12.2 seconds.