The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  0  1  1  1  1  1  2  X  X  1  X  1  0  1  1  1  0  1  X  1  X  X  X  1  1  0  1  1  1  0  X  X  0  1  1  X  X  2  X  1
 0  X  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2 X+2  2  0  2 X+2  X  X  2  X X+2 X+2  0  2  0  X  0 X+2 X+2 X+2 X+2  0  2  2  0  X  2  2  0  X  2 X+2  2  0  X  2  X X+2  0 X+2  X X+2  0 X+2  X  2 X+2  2  2  X X+2  2 X+2  2 X+2 X+2  0  2  X  X X+2  X  0  0
 0  0  X  0  0  0  X X+2 X+2  X  X  2 X+2  X  0  2  0 X+2 X+2  0  X  X  X  0  2  X  2  2 X+2 X+2  0  0  2  X X+2  0  X  2  2  X  2 X+2  X  X  0  0 X+2  X  2 X+2  0  2 X+2  2  0  2  0  2  2 X+2  2  2  0 X+2  2  X  X  X  2 X+2  2 X+2  0  2  2 X+2  2  0
 0  0  0  X  0  X  X  X  0  2  0  X X+2  X  X X+2  2  0  0  2 X+2  X  X  2  0  2 X+2  2  X  0 X+2  X X+2 X+2  2 X+2  X  X  X  0  0  X  0 X+2  X  0  2 X+2  2  X  X X+2 X+2  0  X X+2 X+2  2  0 X+2  X X+2 X+2  X  X  0  X  2  0  X  X X+2 X+2  X  2  X  2  0
 0  0  0  0  X  X  2 X+2  X  2  X  0  X  2 X+2  2  0  0  X X+2  X  0  2 X+2  2  X  0  X  X  0  X X+2 X+2  0  2  0  X  X  2  0 X+2  2 X+2 X+2 X+2  2 X+2  X X+2  X  2 X+2 X+2  X  0  0 X+2  0  2  X X+2  0  2  X  2  0  2  2  0 X+2 X+2 X+2  2  0  X X+2 X+2 X+2
 0  0  0  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  0  2  0  2  0  2  0  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  2  2  0  2  2  2  2  2  2  2  0  2  2  0  0  0  2  0

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+60x^69+109x^70+162x^71+197x^72+246x^73+262x^74+246x^75+321x^76+338x^77+366x^78+378x^79+302x^80+250x^81+189x^82+146x^83+144x^84+84x^85+72x^86+58x^87+39x^88+36x^89+21x^90+28x^91+19x^92+10x^93+5x^94+6x^95+1x^112

The gray image is a code over GF(2) with n=312, k=12 and d=138.
This code was found by Heurico 1.16 in 1.75 seconds.