The generator matrix

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

generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+64x^13+279x^14+586x^15+1099x^16+1838x^17+2702x^18+3176x^19+2756x^20+1932x^21+1089x^22+522x^23+240x^24+70x^25+25x^26+4x^27+1x^34

The gray image is a code over GF(2) with n=76, k=14 and d=26.
This code was found by Heurico 1.16 in 1.86 seconds.