The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+540x^178+339x^180+816x^182+339x^184+648x^186+81x^188+432x^190+45x^192+444x^194+171x^196+192x^198+39x^200+3x^204+6x^212

The gray image is a linear code over GF(4) with n=248, k=6 and d=178.
This code was found by Heurico 1.16 in 16 seconds.