The generator matrix
1 0 1 1 1 1 1 1
0 1 1 a a+1 0 0 0
0 0 (a+1)X 0 0 X 0 X
0 0 0 X 0 (a+1)X (a+1)X (a+1)X
0 0 0 0 (a+1)X X aX 0
generates a code of length 8 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+51x^12+219x^16+846x^20+3072x^21+1626x^24+9216x^25+1263x^28+90x^32
The gray image is a linear code over GF(4) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.0313 seconds.