The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+264x^57+108x^58+612x^59+1098x^60+1788x^61+1716x^62+4188x^63+4566x^64+7248x^65+5832x^66+11160x^67+13065x^68+18456x^69+14904x^70+25128x^71+24351x^72+26760x^73+19020x^74+25476x^75+19602x^76+17484x^77+7572x^78+7164x^79+2724x^80+1728x^81+69x^84+51x^88+6x^92+3x^96

The gray image is a linear code over GF(4) with n=96, k=9 and d=57.
This code was found by Heurico 1.16 in 65.1 seconds.