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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+16x^70+84x^72+122x^74+64x^75+94x^76+384x^77+52x^78+64x^79+26x^80+44x^82+26x^84+20x^86+24x^88+2x^90+1x^144

The gray image is a code over GF(2) with n=308, k=10 and d=140.
This code was found by Heurico 1.16 in 0.402 seconds.