The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+321x^60+492x^61+324x^62+804x^63+2214x^64+1872x^65+1212x^66+1956x^67+5010x^68+3924x^69+2628x^70+5004x^71+9069x^72+6108x^73+3636x^74+5100x^75+7581x^76+4080x^77+1416x^78+960x^79+1377x^80+420x^81+24x^84+3x^88

The gray image is a linear code over GF(4) with n=96, k=8 and d=60.
This code was found by Heurico 1.16 in 4.94 seconds.