The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+174x^172+468x^173+435x^176+1524x^177+573x^180+1824x^181+864x^184+2784x^185+1008x^188+2916x^189+627x^192+1956x^193+225x^196+744x^197+39x^200+72x^201+54x^204+33x^208+24x^212+27x^216+6x^220+6x^224

The gray image is a linear code over GF(4) with n=248, k=7 and d=172.
This code was found by Heurico 1.16 in 77.7 seconds.