The generator matrix

 1  0  0  1  1  1  1 a^2*X  1  1  1  1  1 a^2*X  1  1  1  X  1  1 a*X  1  1  1
 0  1  0 a^2*X a*X a^2*X+1  1  1 X+1  a a*X+a X+a  X  1 a^2 X+a^2 a*X+a^2  1 a*X+1 a^2*X+a  1 X+a  X a*X+a
 0  0  1  1  a X+a X+1 a^2 a*X+a^2 a*X a^2*X+a a^2*X+a^2 X+a^2 a*X+1 a*X+a a*X+1  X a^2*X+a a^2*X X+1 a*X+a  1 a*X+a^2 X+a^2

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+420x^66+216x^67+228x^68+480x^69+588x^70+264x^71+174x^72+444x^74+168x^75+228x^76+288x^77+468x^78+120x^79+9x^80

The gray image is a linear code over GF(4) with n=96, k=6 and d=66.
This code was found by Heurico 1.16 in 0.235 seconds.