The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+732x^63+330x^64+2244x^67+873x^68+3852x^71+1536x^72+4140x^75+1212x^76+1320x^79+111x^80+21x^84+6x^88+6x^92

The gray image is a linear code over GF(4) with n=96, k=7 and d=63.
This code was found by Heurico 1.16 in 0.352 seconds.