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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+141x^84+192x^85+96x^86+405x^88+396x^89+192x^90+426x^92+348x^93+288x^94+549x^96+420x^97+192x^98+240x^100+180x^101+12x^104+6x^108+6x^112+3x^116+3x^120

The gray image is a linear code over GF(4) with n=124, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0411 seconds.