The generator matrix
1 0 1 1 1 1 1 1
0 1 1 0 a^2*X+1 X a^2*X+1 a
0 0 a^2*X X a*X a^2*X 0 X
generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+72x^19+21x^20+96x^21+144x^23+213x^24+288x^25+168x^27+15x^28+6x^32
The gray image is a linear code over GF(4) with n=32, k=5 and d=19.
This code was found by Heurico 1.16 in 0 seconds.