The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+189x^60+48x^61+48x^63+897x^64+288x^65+432x^67+1887x^68+768x^69+1296x^71+3759x^72+1248x^73+1296x^75+2952x^76+720x^77+408x^80+99x^84+39x^88+9x^92

The gray image is a linear code over GF(4) with n=96, k=7 and d=60.
This code was found by Heurico 1.16 in 0.425 seconds.