The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2 X+2  1 X+2  1  1  1  0  1  1  1  1  2  2 X+2  2  X  0 X+2  2  X  1  1  1  1  1  1  1  1  1  1  2  X  1  1  X  0 X+2  1  1  0  X  X  1  X  1  1  1  1  1  1  1  X  1  1  0 X+2  1  1  0  0  1  2  1  2
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X+2  2  X X+1  3  0 X+2  0 X+2  1  1 X+3  1 X+2  1  1  3 X+3  1  1  1  0  1  1 X+1 X+2 X+2  X X+3  0  1  2  3  1  1 X+1 X+2  1  1  3  0 X+2  1
 0  0  X  0 X+2  0  X  2  X X+2  0 X+2  2  2  X  2  X  X  0 X+2 X+2  2  0 X+2  2  0  X  X  0  0  X  X  0  0  X  X  2  2  0  0  X  X  0  2 X+2 X+2 X+2 X+2 X+2 X+2 X+2  X  X X+2 X+2  2  2  0  2  X  X  X X+2  2 X+2  X  X X+2 X+2  0  X X+2  0  X X+2  0
 0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  2  2  2  0  2  2  2  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  2  2  2  2  2  0  2  0  0  0  0  0  2  0  2  2  0  0  2  0  0  0
 0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+127x^70+80x^71+314x^72+108x^73+261x^74+76x^75+232x^76+88x^77+244x^78+72x^79+172x^80+60x^81+108x^82+28x^83+38x^84+21x^86+5x^88+7x^90+4x^92+1x^100+1x^108

The gray image is a code over GF(2) with n=304, k=11 and d=140.
This code was found by Heurico 1.16 in 0.553 seconds.