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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+37x^70+66x^71+91x^72+98x^73+127x^74+162x^75+195x^76+224x^77+176x^78+182x^79+170x^80+146x^81+117x^82+84x^83+30x^84+20x^85+35x^86+12x^87+22x^88+16x^89+19x^90+6x^91+2x^92+8x^93+1x^100+1x^130

The gray image is a code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 0.675 seconds.