The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+219x^76+336x^77+72x^78+384x^79+1482x^80+1500x^81+348x^82+1536x^83+3426x^84+3588x^85+528x^86+3648x^87+6942x^88+6168x^89+984x^90+5952x^91+8118x^92+6936x^93+840x^94+3648x^95+4662x^96+2892x^97+300x^98+192x^99+633x^100+84x^101+72x^104+33x^108+9x^112+3x^116

The gray image is a linear code over GF(4) with n=120, k=8 and d=76.
This code was found by Heurico 1.16 in 7.28 seconds.