The generator matrix
1 0 1 1 1 X^2+X 1 1 X^2+2 1 1 X+2 1 1 1 1 X X 1
0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 3 1 0 X^2+X X^2+2 X+2 0 0 0
0 0 2 0 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0
0 0 0 2 0 0 2 2 0 2 0 2 0 2 2 0 2 2 0
0 0 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 2 0
0 0 0 0 0 2 0 2 2 2 0 2 2 2 0 0 0 0 0
generates a code of length 19 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+40x^14+52x^15+105x^16+372x^17+1152x^18+680x^19+1128x^20+392x^21+72x^22+36x^23+46x^24+4x^25+16x^26
The gray image is a code over GF(2) with n=152, k=12 and d=56.
This code was found by Heurico 1.16 in 0.046 seconds.