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

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+579x^60+636x^62+2370x^64+972x^66+3567x^68+1908x^70+4089x^72+1092x^74+1125x^76+33x^80+9x^84+3x^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 0.465 seconds.