The generator matrix

 1  0  0  1  1  1 a^2*X  1  1  1  1  1  1  1 a^2*X  1  0  1  1 a^2*X  1 a*X  1
 0  1  0  1  a a^2  1 a^2*X a^2*X a^2*X+1 a^2*X+a^2  1 a^2*X+1 a*X  1  1  1  0 a^2*X+a  1  0  1 a^2*X+1
 0  0  1 a^2  a  1 a*X+1  1 a^2 a*X  X X+1  X a*X+1 X+1 a^2*X+a a*X+a X+a X+1  a X+a a^2*X+1 X+1
 0  0  0  X  0  X  0 a*X a^2*X a*X a^2*X a^2*X  0 a^2*X a*X a*X  X a*X  X a^2*X  0 a^2*X a^2*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+651x^60+588x^62+2250x^64+1020x^66+3576x^68+1956x^70+4152x^72+1044x^74+1095x^76+39x^80+6x^84+6x^88

The gray image is a linear code over GF(4) with n=92, k=7 and d=60.
This code was found by Heurico 1.16 in 0.297 seconds.