The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1 1
0 2 0 0 0 0 0 0 0 2 0 2 2 0
0 0 2 0 0 0 0 0 0 2 2 2 0 0
0 0 0 2 0 0 0 0 0 2 2 0 2 0
0 0 0 0 2 0 0 0 2 2 0 0 2 0
0 0 0 0 0 2 0 0 2 0 0 2 2 0
0 0 0 0 0 0 2 0 2 0 2 2 0 0
0 0 0 0 0 0 0 2 2 2 2 0 0 0
generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+38x^8+17x^10+52x^12+128x^13+1580x^14+128x^15+33x^16+54x^18+4x^20+12x^22+1x^26
The gray image is a code over GF(2) with n=112, k=11 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.