The generator matrix

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

generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+468x^69+660x^70+348x^71+1119x^72+1860x^73+2136x^74+1320x^75+2994x^76+3912x^77+4212x^78+3168x^79+4803x^80+6216x^81+6252x^82+4440x^83+5649x^84+5988x^85+4488x^86+1476x^87+1785x^88+1524x^89+684x^90+12x^92+12x^96+9x^100

The gray image is a linear code over GF(4) with n=108, k=8 and d=69.
This code was found by Heurico 1.16 in 6.4 seconds.