The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+348x^57+192x^58+480x^59+1083x^60+1788x^61+1056x^62+2172x^63+2586x^64+4260x^65+3072x^66+4140x^67+5379x^68+7476x^69+5280x^70+6324x^71+5853x^72+6384x^73+2688x^74+2244x^75+1449x^76+1248x^77+21x^80+9x^84+3x^88

The gray image is a linear code over GF(4) with n=92, k=8 and d=57.
This code was found by Heurico 1.16 in 4.49 seconds.