The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+99x^60+108x^61+48x^63+486x^64+144x^65+288x^67+867x^68+264x^69+432x^71+933x^72+144x^73+129x^76+108x^77+33x^80+9x^84+3x^88

The gray image is a linear code over GF(4) with n=92, k=6 and d=60.
This code was found by Heurico 1.16 in 0.028 seconds.