The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+104x^64+8x^65+80x^66+108x^67+389x^68+460x^69+288x^70+1048x^71+540x^72+1856x^73+400x^74+2664x^75+586x^76+2664x^77+400x^78+1856x^79+480x^80+1048x^81+288x^82+460x^83+305x^84+108x^85+80x^86+8x^87+93x^88+40x^92+13x^96+8x^100+1x^104

The gray image is a code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 19.1 seconds.