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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+39x^68+50x^69+85x^70+114x^71+117x^72+164x^73+203x^74+216x^75+208x^76+208x^77+145x^78+138x^79+110x^80+62x^81+47x^82+24x^83+26x^84+18x^85+20x^86+16x^87+8x^88+10x^89+10x^90+4x^91+3x^92+1x^94+1x^126

The gray image is a code over GF(2) with n=304, k=11 and d=136.
This code was found by Heurico 1.16 in 0.635 seconds.