The generator matrix

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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+1110x^172+3093x^176+3672x^180+3282x^184+2532x^188+1623x^192+936x^196+126x^200+6x^204+3x^208

The gray image is a linear code over GF(4) with n=244, k=7 and d=172.
This code was found by Heurico 1.16 in 1.42 seconds.