The generator matrix
1 0 1 1 1 1
0 1 1 0 0 0
0 0 a^2*X 0 0 0
0 0 0 X 0 0
0 0 0 0 X 0
0 0 0 0 0 X
generates a code of length 6 over F4[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+18x^4+48x^6+135x^8+576x^10+540x^12+2592x^14+6144x^15+1215x^16+29760x^18+18432x^19+1458x^20+3888x^22+729x^24
The gray image is a linear code over GF(4) with n=24, k=8 and d=4.
This code was found by Heurico 1.16 in 0.21 seconds.