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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+168x^66+361x^68+92x^69+606x^70+156x^71+766x^72+328x^73+860x^74+372x^75+859x^76+552x^77+830x^78+324x^79+609x^80+168x^81+454x^82+44x^83+293x^84+12x^85+172x^86+104x^88+38x^90+14x^92+8x^94+1x^108

The gray image is a code over GF(2) with n=304, k=13 and d=132.
This code was found by Heurico 1.16 in 7.04 seconds.